IN   MEMORIAM 
FLOR1AN  CAJO 


StAA^ 


^v? 


COMPLETE   ARITHMETIC 


BY 


SAMUEL    HAMILTON,    Ph.D. 
*» 

SUPERINTENDENT    OF   SCHOOLS,    ALLEGHENY   COUNTY,    PA. 
AND   AUTHOR   OF   "THE   RECITATION" 


NEW   YORK  •:•  CINCINNATI  •:■  CHICAGO 

AMERICAN    BOOK    COMPANY 


Copyright,  190S,  1900,  by 
SAMUEL  HAMILTON. 

Entered  at  Stationers'  Hall,  London. 


HAM.    COMPLETE    ARITH. 

w.  p.    3 

ORI 


PREFACE 

A  complete  arithmetic  should  meet  all  the  ordinary  de- 
mands of  the  elementary  school.  It  may  omit  that  which 
is  non-essential  and  all  matter  that  properly  belongs  to  text- 
books for  secondary  schools ;  but  it  should  include  a  full 
treatment  of  all  important  topics  taught  in  the  elementary 
school,  and  a  limited  treatment  of  those  of  minor  importance. 

This  book  is  intended  for  a  complete  arithmetic,  to  be 
used  either  with  or  without  the  author's  Elementary  Arith- 
metic. The  work  is  divided  into  three  parts.  Part  One, 
after  giving  a  complete  treatment  of  the  fundamental  opera- 
tions, covers  the  work  ordinarily  found  in  the -sixth  year. 
Part  Tioo,  after  reviewing  the  subjects  of  Bills  and  Accounts, 
Denominate  Numbers,  and  Practical  Measurements,  covers 
the  work  of  the  seventh  year.  Part  Three  covers  the  work 
of  the  eighth  year. 

The  aim  of  this  book  is  threefold : 

(1)  To  give  the  pupil  skill  in  the  art  of  computation. 

(2)  To  make  him  a  good  mathematician. 

(3)  To  give  him  a  working  knowledge  of  modern  business 
methods. 

The  first  necessarily  suggests  an  abundance  of  graded 
work. 

The  second  requires  both  inductive  and  deductive  thought. 
The  method,  therefore,  is  inductive  in  the  development  of 
all  mathematical  principles,  and  deductive  in  their  applica- 
tion.     It  requires  also  that  all  solutions  shall  be  clear  and 

918185 


4  PREFACE 

concise,  and  that  the  statements  of  all  definitions,  rules,  and 
principles  shall  be  as  brief  and  comprehensive  as  possible. 

The  third  aim  demands  a  practical  treatment  of  all  sub- 
jects from  the  standpoint  of  actual  business  methods. 

With  these  ends  in  view,  attention  is  invited  to  the 
following : 

1.  The  large  number  of  graded  problems  under  each  sub- 
ject and  in  the  reviews. 

2.  The  abundance  of  exercises  for  oral  drill. 

3.  The  study  of  problems  and  processes. 

4.  The  treatment  of  Fractions,  Practical  Measurements, 
and  the  Comparative  Studies  in  Percentage. 

5.  The  problems  arising  out  of  business  conditions. 

6.  The  treatment  of  Promissory  Notes,  Banking,  Com- 
mercial Discount,  Exchange,  and  Stocks  and  Bonds  accord- 
ing to  the  actual  methods  of  modern  business. 

The  author  gratefully  acknowledges  his  indebtedness  to 
many  prominent  educators  and  friends  for  valuable  aid,  dis- 
criminating criticisms,  and  helpful  suggestions. 

SAMUEL   HAMILTON. 


CONTENTS 

PART   I  — SIXTH   YEAR 


Fundamental  Processes  .     .     . 
Arabic    System  of    Notation 

and  Numeration        .     . 
Roman   System  of   Notation 

and  Numeration  .... 
United  States  Money    .     .     . 

Addition 

Subtraction 

Multiplication 

Division 

Combining  Processes   .     .     . 

Factors  and  Divisors  .... 
Tests  of  Divisibility      .     .     . 

Factoring 

Greatest  Common  Divisor 
Least  Common  Multiple   .     . 
Cancellation 


PAGE 

7 

8 

11 
12 
13 
19 
23 
29 
36 

37 
38 
39 
40 
41 
42 


Fractions 44 

Fractional  Units       ....  44 
Reading  and   Writing   Frac- 
tions    40 

Reduction 47 

Addition  and  Subtraction      .  52 

Multiplication 58 

Fractional  Parts  of  Fractions  05 

Division 08 

Complex  Fractions  ....  75 

Fractional  Relations     ...  70 

Review 78 

Problems  for  Analysis     ...  84 

Decimal  Fractions 90 

Notation  and  Numeration      .  91 
Common  Fractions  and  Deci- 
mals    94 

Addition  and  Subtraction      .  90 


Multiplication 98 

Division 101 

Changing  Fractions  to  Deci- 
mals    100 

Review 107 

Business      Applications      of 

Decimals 108 


Simple  Accounts 

Denominate  Numbers      .     .     . 

Standard  Units 

Reduction 

Addition  and  Subtraction 
Multiplication  and  Division  . 
Review  of  Denominate  Num- 
bers     

Practical  Measurements  .     .     . 

Length 

Surface 

Painting  and  Kalsomining     . 
The  Right  Triangle .     .     .     . 


Volume 
Practical  Applications 
Lumber      .... 
Review  Problems     . 


Percentage     .... 

Commission     .     . 
Commercial  Discount 


112 

115 

115 
110 
119 
121 

122 

123 
123 
124 

128 
128 
130 
132 
134 
138 

141 
147 
148 


Interest 151 


Review  of  Percentage  and  In- 
terest       

Receipts  and  Checks  .     .     .     . 

General  Review 


155 
157 
159 


PART   II  — SEVENTH   YEAR 


Bills  and  Accounts      .     .     .     .     166 

Receipts 166 

Ordering  Goods 1H7 


Receipted  Bills 108 

Accounts 170 

Ledger  Accounts      ....     173 


6 


CONTENTS 


PAGE 

Denominate  Numbers      .     .     .  175 

Reduction 175 

Foreign  Money 18  i 

Addition  and  Subtraction      .  184 

Multiplication  and  Division  .  186 

Review  Problems 188 

Practical  Measurements  .     .     .  192 

Length  and  Surface      .     .     .  192 

Lines  and  Angles     .     .     .     .  194 

Triangles 196 

Quadrilaterals 198 

Rectangles 199 

Plastering  and  Painting    .     .  201 
Roofing  and  Flooring   .     .     .  2<>2 
Papering  and  Carpeting    .     .  2i)4 
Areas  of  Triangles,   Quadri- 
laterals, and  Circles  .     .     .  2(16 

Solids 212 

Lumber 217 

Concrete,   Stone,  and   Brick- 
work    220 

The  Cylinder 221 

Bins,  Tanks,  and  Cisterns     .  223 


PAGE 

Approximate  Measurements  .  224 

Review  Problems     ....  225 

Analysis 231 

The  Equation 231 

Percentage 237 

Review 247 

Gain  and  Loss 249 

Review  ........  253 

Commission  and  Brokerage  .  255 

Insurance 259 

Commercial  Discount  .     .     .  264 

Commercial  Bills      ....  2i>8 

Local  and  State  Taxes .     .     .  269 

Duties  or  Customs   ....  272 

Interest 275 

Simple  Interest 275 

Problems  in  Simple  Interest  .  283 

Annual  Interest 286 

Exact  Interest 287 

Compound  Interest ....  288 

Savings  Accounts     ....  289 

Investments 291 

Promissory  Notes     ....  292 

Partial  Payments  of  Notes     .  298 


PART   III  — EIGHTH    YEAR 


Banks  and  Banking     ....  303 

Bank  Discount 307 

Exchange 315 

Stocks  and  Bonds 324 

Stocks 324 

Bonds 331 

Test  Problems  in  Percentage    .  335 

Ratio  and  Proportion  ....  337 

Ratio 337 

Simple  Proportion    ....  338 
Partitive  Proportion  and  Part- 
nership      341 

Problems  for  Oral  and  Written 

Analysis 345 

Longitude  and  Time    ....  349 

Government  Land  Measures      .  356 

Powers  and  Roots 358 

Extracting  Roots      ....  360 


Square  Root 

Mensuration 

Regular  Polygons     .... 

Solids 

Similar  Surfaces 

Similar  Solids 

Specific  Gravity 

Review 

Metric  System 

Agricultural  Problems     .     .     . 

Test  Problems 

General  Review 

Optional  Subjects 

Present  Worth  and  True  Dis- 
count        

Foreign  Exchange   .... 

Compound  Proportion .     .     . 

Cube  Root 

Reference  Tables 

Index  


361 
367 
367 
368 
376 
378 
879 
381 
382 
392 
401 
406 


421 
422 
425 
426 

433 

437 


COMPLETE  ARITHMETIC 

PART   I  — SIXTH    YEAR 

FUNDAMENTAL   PROCESSES 

NOTATION  AND   NUMERATION 

A  unit  is  a  single  thing ;  as,  one,  one  cent. 

A  number  is  a  unit  or  a  collection  of  units. 

Numbers  are  used  to  tell  how  many ;  they  are  expressed 
by  figures  or  letters.  The  figures  we  now  use  are  of  Hindu 
origin,  but  the  Arabs  were  the  first  people  to  introduce  them 
into  Europe.     They  are 

Naught        One        Two        Three        Four        Five        Six        Seven        Eight        Nine 
012  34567  89 

These  ten  figures  are,  therefore,  called  Arabic  numerals. 

The  figure  o  is  called  naught,  zero,  or  cipher,  and  has  no 
value. 

The  Arabic  notation  is  a  method  of  expressing  numbers 
by  means  of  figures. 

Numeration  is  a  method  of  reading  numbers  expressed  by 
means  of  figures  or  letters. 

Arithmetic  is  the  science  of  numbers  and  the  art  of  com- 
puting by  them. 

7 


8  FUNDAMENTAL   PROCESSES 

ARABIC. SYSTEM  OF  NOTATION  AND  NUMERATION 

Any  number  containing  but  one  figure,  simply  stands  for 
so  many  ones;  thus,  9  stands  for  9  units,  or  ones. 

In  any  number  containing  two  figures,  the  first  place  at  the 
right  is  called  ones ;  the  second  place  is  called  tens ;  thus, 
in  25  there  are  2  tens,  or  20  ones,  plus  5  ones,  or  25  ones. 
25  is  read,  "twenty-five." 

1.  Name  the  ones  and  tens  in  the  following  numbers  and 
then  state  how  many  ones  each  number  equals : 

15   25    30    75    82    60    72    45    70    99    20    10    39    47    90 

In  any  number  containing  three  figures,  the  third  place 
from  the  right  is  called  hundreds;  thus,  in  325,  the  3  stands 
for  300  ones.     325  is  read,  "three  hundred  twenty-five." 

2.  Name  the  ones,  tens,  and  hundreds  in  the  following  and 
then  state  how  many  ones  each  number  equals: 

125      329      879      801      600      650      803      132      400    '  904 
109      705      105      550      900      901      502      999      570      809 

In  any  number  containing  four  figures,  the  fourth  place 
from  the  right  is  called  thousands.  4635  is  read,  "  four  thou- 
sand, six  hundred,  thirty-five." 

3.  Name  the  places  in  each  number  and  then  read: 

2135    6005   6910   5604    5000   4025    2684   8709   7009    8900 
For  convenience  in  reading  large  numbers,  in  the  Arabic 
system,  the  figures  are  generally  separated  by  commas  into 
groups  of  three  figures  each,  called  periods. 

The  first  period,  counting  from  the  right,  is  units;  the 
second,  thousands;  the  third,  millions;  the  fourth,  billions; 
the  fifth,  trillions  ;  etc. 


NOTATION   AND   NUMERATION 


9 


The    following   table    shows    the    arrangement    of    these 
periods,  and  the  three  orders  of  figures  in  each  period: 


TRILLIONS' 

BILLIONS' 

MILLIONS' 

THOUSANDS' 

UNITS* 

PERIOD 

PERIOD 

PERIOD 

PERIOD 

PERIOD 

O 

U 

(A 

c 

c 

c 

<tf 

o 

o 

o 

n 

V* 

3 

73 

~         y> 

zz 

« 

« 

(/> 

o 

C 

I         o 

15 

c 
o 

E 

c 
o 

of 

(A 

T3 

to 

*U         — 

w» 

*D 

-o 

— * 

TO 

j* 

C 

"O 

c 
o 

2 

T3 

15 

c 
o 

0) 

E 

c 
o 

0) 

(4 
to 

3 

E      c 

~ 

C 

c 

™ 

C 

C 

■f™ 

c 

C 

O 

c 

2     S 

3           0, 

"C 

3 

<u 

~ 

3 

0) 

3 

© 

J= 

D 

o       c 

X       H 

1- 

X 

h- 

00 

I 

1- 

2 

X 

H 

h- 

X 

1-     o 

1    0 

1  . 

3 

4 

5    , 

6 

4 

2 

,    o 

0 

1       , 

3 

4    6 

The  number  in  the  table  is  read,  "  101  trillion,  345  billion, 
642  million,  1  thousand,  346." 

The  ones  are  not  named  in  reading  numbers. 

Since  ten  ones  make  1  ten,  and  ten  tens  make  1  hundred,, 
etc.,  our  system  of  writing  numbers  is  called  a  decimal  sys- 
tem. The  word  decimal  comes  from  the  word  decern,  mean- 
ing ten. 

Name  the  places  and  periods,  then  read : 


4. 

129,475 

8. 

1,700,425  pounds 

12.      400,000,000 

5. 

407,575 

9. 

9,609,500  tons 

13.       709,050,050 

6. 

600,905 

10. 

5,505,608  yards 

14.    8,000,000,000 

7. 

790,505 

11. 

40,000,905  dollars 

15.    9,075,074,093 

1 

Copy,  point  off,  then  read: 

16. 

700102 

23.          5050504 

30.             60414 

17. 

6067004 

24.        12126012 

31.           102365 

18. 

8011100 

25.        87649101 

32.        14763 1ST 

19. 

90314607 

26.      104706950 

33.      243540038 

20. 

910723586 

27.    120243(U14 

34.    2452603467 

21. 

837421012 

28.    3183456109 

35.    8703005020 

22. 

987654321 

29.    7891234560 

36.    6010100100 

10  FUNDAMENTAL   PROCESSES 

Writing  Numbers 
Write : 

1.  25  million,  161  thousand,  104. 

2.  2  million,  12  thousand,  8. 

3.  36  million,  1  thousand,  109. 

4.  300  billion,  304  million,  100  thousand,  40. 

5.  16  billion,  9  million,  70  thousand,  700. 

6.  26  million,  18  thousand,  9. 

7.  7  billion,  46  million,  900  thousand,  90. 

8.  74  billion,  7  million,  46  thousand,  809. 

9.  Two  hundred  six  thousand,  eight. 

10.  Twenty-five  million,  six  hundred. 

11.  One-thousand  thousand. 

Write  each  of  the  numbers  12  to    23,  first,  when    10    is 
added,  and  second,  when  10  is  subtracted  from  each  number. 

12.  80,900      15.    60,804      is.    497,842      21.    50,001 

13.  67,895      16.    50,000      19.    109,090      22.    70,080 

14.  45,101      17.    70,800      20.    290,009      23.    59,009 

24.  One  million,  two  hundred  thousand. 

25.  Nine  billion,  six-hundred  million,  seven. 

26.  Six  billion,  six  thousand,  six  hundred  six. 

27.  Seven  hundred  nine  thousand,  two. 

28.  Sixty-nine  million,  eight  thousand. 

29.  Nine  hundred  two  million,  forty-two  thousand,  sixty-two 

30.  Thirty-two  thousand,  thirty-two. 

31.  Six-hundred  forty-four  million,  six  hundred  four. 

32.  Ten  thousand,  ten. 

33.  Fifteen  hundred  million. 

34.  Twenty-eight  million,  eight  thousand,  eight. 


ROMAN   NOTATION 


11 


ROMAN   SYSTEM   OF   NOTATION   AND   NUMERATION 

The  seven  letters  used  in  Roman  notation  are  : 

I         V        X         L        C         D         M 

1         5        10        50      100     500     1000 

The  other  numbers  are  represented  by  combinations  thus : 

I.  When  a  letter  is  followed  by  the  same  letter  or  by  one 
of  less  value,  the  values  of  the  letters  are  to  be  added.  Thus, 
XX  represents  20  ;   XI  represents  11. 

II.  When  a  letter  is  followed  by  one  of  greater  value,  the 
value  of  the  smaller  is  to  be  subtracted  from  that  of  the  greater. 
Thus,  IV  represents  4;   IX  represents  9. 

III.  When  a  letter  is  placed  between  two  letters  of  greater 
value,  the  value  of  the  smaller  is  to  be  subtracted  from  the  sum 
of  the  other  two.  Thus,  XIV  represents  14;  XIX  represents 
19. 

A  bar  placed  over  a  letter  multiplies  its  value  by  1000.  Thus, 
V  represents  5000. 

The  following  table  further  illustrates  the  system  : 


1,1 

VIII,    8 

XVI,  16 

LXXX,    80 

DCC,  700 

11,2 

IX,    9 

XX,  20 

XC,    90 

DCCC,  800 

111,3 

X,  10 

XXX,  30 

C,  100 

CM,  900 

IV,  4 

XI,  11 

XL,  40 

CCC,  300 

M,  1000 

V,5 

XII,  12 

L,  50 

CD,  400 

MCM,  1900 

VI,  6 

XIV,  14 

LX,  60 

D,  500 

V,  5000 

VII,  7 

XV,  15 

LXX,  70 

DC,  600 

M,  1,000,000 

Read : 

1.  XLIII        CDXLIX         MDII  MCDXCII 

2.  XCIX        MCMVIII        MDLXXVI        MDCCCLXI 

3.  Express  in  Roman  notation:    41,  63,  84,  99,  107,  218, 
572,  735,  996,  1907,  1564,  1616,  1000,  260,000. 


12  FUNDAMENTAL   PROCESSES 

UNITED  STATES   MONEY 


10  mills  =  1  cent 
10  cents  =  1  dime 


10  dimes  =  1  dollar 
10  dollars  =  1  eagle 


1.  From  the  above  table,  tell  why  our  money  is  a  decimal 
system  of  money. 

The  dollar  sign  is  $ ;  it  is  placed  before  the  number  of 
dollars.  The  sign  for  cent  or  cents  is  $ ;  it  is  placed  after 
the  number  of  cents. 

When  dollars  and  parts  of  a  dollar  are  written  as  one 
number,  a  period,  called  a  decimal  point,  separates  the  dollars 
from  the  cents  ;  thus,  8  dollars,  15  cents  is  written  $8.15. 

Parts  of  a  dollar  may  be  written  in  three  ways ;  thus,  15  cents  may  be 
written  15?,  §0.15,  or  $.15. 

The  first  two  places  to  the  right  of  the  decimal  point  are 
for  cents. 

2.  Read  in  as  many  ways  as  you  can  : 

15^      18.32      5/  105^       10.99     $.25        $0.50 

900/       $.01      $0.35      $0.05      100^       1101/      $9.90 

The  first  place  to  the  right  of  the  point  is  for  dimes, 
or  tenths  of  a  dollar  ;  the  second,  for  cents,  or  hundredths 
of  a  dollar ;  the  third,  for  mills,  or  thousandths  of  a  dollar. 
$.025  is  read,  "two  cents,  five  mills." 

3.  Read : 

$.02  $8.06  $.901  $.515 

8.022  $9,055  $.80  $.005 

$.255  $1,005  $.801  $.50 

4.  Read,  then  write  from  dictation,  using  the  dollar  sign: 
$2.50  275  dollars,  5  cents  100  cents,  8  mills 
80.75               89  dollars,  2  mills  525  cents,  5  mills 
85.05               10  dollars,  1  cent               875  cents,  3  mills 


ADDITION 


13 


ADDITION 

1.  Count  by  2's  to  100  ;  by  3's  to  00  ;  by  4's  to  100. 

2.  Count  by  6's  to  102;   by  7's  to  105  ;   by  8's  to  104. 

3.  Count  by  9's  to  108;   by  ll's  to  143;  by  12's  to  168. 

Addition  is  the  process  of  uniting  two  or  more  numbers 
to  form  one  number. 

The  sign  +,  called  plus,  indicates  addition;  the  sign  =, 
called  equal  or  equals,  indicates  equality. 

Announce  the  sums  at  sight: 


4. 

5. 

.   6. 

7. 

8. 

9. 

5  +  7 

9  +  9 

1  +  3 

8  +  6 

2  +  2 

2+8 

1  +  6 

1  +  4 

2  +  9 

9  +  8 

4  +  6 

4  +  2 

3  +  3 

6  +  2 

9+1 

7  +  2 

6+7 

9  +  4 

0  +  6 

9  +  3 

7  +  3 

8  +  7 

8  +  0 

0  +  9 

6  +  6 

2  +  1 

8  +  5 

4  +  4 

2  +  3 

3  +  4 

1  +  8 

5  +  4 

7  +  2 

5  +  6 

6  +  3 

8+4 

7  +  9 

5  +  2 

5  +  5 

0  +  4 

7  +  7 

3  +  8 

5  +  3 

1  +  1 

9  +  5 

7  +  4 

8  +  8 

5  +  1 

Announce  the  sums  at  sight,  first  in  rows  across,  then  in 
columns  : 


10. 

11. 

12. 

13. 

14. 

15. 

16 

17. 

154 

534 

561 

147 

964 

275 

784 

368 

371 

826 

729 

684 

837 

984 

926 

574 

723 

943 

358 

493 

496. 

532 

578 

397 

In  like  manner,  announce  tli 

e  sums : 

18.       19.        20. 

21.       22.       23. 

4356 

97t;5 

3742 

8674 

7248 

5632 

8547 

6934 

9746 

7897 

6754 

9985 

7961 

9847 

6957 

8753 

3976 

7987 

5943 

41 

)57 

6582 

7541 

) 

6< 

)37 

9147 

14 


FUNDAMENTAL   PROCESSES 


The  addends  in  addition  are  the  numbers  to  be  added. 

The  sum  or  amount  is  the  result  of  addition. 

Like  numbers  are  numbers  that  express  the  same  units ; 
as,  3  pounds,  5  pounds,  or  3,  5. 

Unlike  numbers  are  numbers  that  express  different  units ; 
as,  7  days,  1 3. 

Only  like  numbers  can  be  added. 

24.  Name  and  add  the  like  numbers  in  the  following: 
$5,  5  ft.,  4  oz.,  $4,  3  oz.,  3  gal.,  6  gal.,  6  ft. 

25.  Name  the  addends  ;  then  give  the  sum  or  amount : 

8753  4        12        5  7        12 

1404        11  99  Oil 

5        2        7         9  7         10         8         12  5 


26.  Add  45  and  23,  thus  :  45  +  23  =  45  +  20  +  3  =  68. 
Add  in  like  manner  : 


27.  55  and  28  =  ?  31. 

28.  29  and  47  =  ?  32. 

29.  31  and  42  =  ?  33. 

30.  57  and  32  =  ?  34. 


34  and  47  =  ? 
69  and  28  = 
49  and  35  = 
44  and  57  = 


Add  the  two  columns,  as  in  problem  26. 


39. 
5 

10 

11 

27 

4 

12 


40. 

7 
15 
20 

4 

9 
12 


41. 

3 

10 

15 

11 

9 

7 


42. 

9 
8 
16 
4 
7 
3 


43. 
11 

12 

14 

10 

5 

7 


44. 
10 

12 

7 
14 

9 

7 


35. 

54  and  36  = 

36. 

72  and  19  = 

37. 

37  and  47  = 

38. 

46  and  53  = 

45. 

15 
10 

4 

9 

7 

10 


46. 
11 

7 
4 
12 
9 
6 


47. 

26 
37 
12 
29 
17 
13 


Note.  —  Practice  on  similar  work,  until  pupils  can  add  rapidly  and 
accurately. 


ADDITION 


15 


Seeing  Groups 
Add,  observing  the  groups  that  make  10,  15,  etc. 


20 


5. 

8 
9 
3 
5 
4 
6 
7 
9 
8 
9 
6 


6. 

3 

9 
8 
2 
7 
8 
5 
4 
2 
1 
3 


7. 

2 
6 
4 
8 
4 
6 
5 
7 
8 
1 
9 


Written  Work 


l.    Find  the  sum  of  325,  436,  285. 

Write  the  numbers  in  their  order,  as 
indicated.  In  adding  the  first  column,  we 
think  5,  11,  16  ones;  then  write  the  6  ones 
and  carry  the  1  ten  to  the  tens'  column. 
9,  12,  14  tens ;  then  write  the  4  tens  and 
carry  the  hundred  to  hundreds'  column. 
3,  7,  10  hundreds.     The  sum  is  1046. 


325 
Addends     436 

285 
Sum 


1046 
Test  by  adding  downwards 

Practice  until  you  can  add  these  problems  rapidl) 


2. 

3. 

4. 

5. 

$729.15 

206793 

534891 

726432 

804.90 

429874 

567321 

874921 

728.16 

358079 

623413 

785341 

574.34 

427451 

347621 

634541 

420.85 

874297 

983122 

442211 

345.78 

298743 

246893 

532891 

16 


FUNDAMENTAL   PROCESSES 


In  adding  two  or  more  columns,  business  men  frequently 
write  the  sum  of  each  column  separately  on  a  slip  of  paper, 
and  then  add  the  separate  sums  as  illustrated  in  problem  6. 
In  case  of  interruption  or  error  it  is  then  not  necessary  to  go 
over  all  the  work. 


6. 

7. 

8. 

9. 

10. 

11. 

279 

224 

746 

581 

910 

375 

874 

921 

317 

841 

725 

421 

398 

234 

567 

789 

234 

291 

569 

321 

104 

902 

803 

123 

768 

572 

571 

846 

931 

146 

343 

937 

847 

641 

261 

143 

41 

921 

803 

731 

283 

197 

39 

321 

830 

450 

847 

190 

28 

731 

476 

903 

275 

913 

3231 

Axld  these 

;  problems  and  test  the  work  in 

9  minutes  : 

12. 

13. 

14. 

15. 

16. 

17. 

56081 

6720 

2954 

3783 

1751 

5068 

2094 

>12   4604 

3261 

5427 

7173 

7504 

8675 

7259 

5050 

7891 

5009 

8795 

6985 

>10   8753 

7406 

5030 

4287 

6474 

3745" 

6758 

2834 

6793 

5783 

2758 

5268 

-20   4326 

6498 

7406 

7205 

6471 

7777 

6734 

5065 

5872 

4987 

2050 

5989 

7583 

8439 

3458 

6034 

6579 

7481 

!     3586 

9823 

7295 

2985 

2068 

5479 

t10   2734 

7984 

8376 

3046 

6579 

8705 

1     4725 

2030 

2794 

1154 

2068 

3074. 

1     6050 

5984 

6384 

3683 

5432 

5547 

1  q   7438 

3749 

6589 

4594 

4280 

6875 

|12   5006 

5308 

7405 

5181 

5683 

ADDITION 


17 


Making  Change. 

Business  men  make  change  by  the  adding  method.  Thus, 
if  a  purchase  is  made  for  11.57,  and  $2.00  is  given  in  pay- 
ment, the  clerk  will  probably  say :  "  One  dollar  fifty-seven 
cents,  sixty,  seventy,  seventy-five,  two  dollars,"  laying  down 
each  time  the  piece  of  money  that  makes  the  sum  named. 

Acting  as  clerk  when  the  following  purchases  and  pay- 
ments are  made,  give  the  exact  language  you  might  use,  if 
the  purchaser  were  actually  present  to  receive  the  change: 


Cost  of 
Purchase 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 
10. 
11. 
12. 
13. 
14. 
15. 


$1.34 
2.95 
2.11 
3.17 
1.15 
4.12 
2.24 
3.54 
1.12 
4.02 
2.79 
2.36 
3.09 
2.71 
3.00 


Amount 
Given 

Cost  of 
Purchase 

$2.00 

16. 

$1.95 

5.00 

17. 

7.23 

3.00 

18. 

3.G7 

4.00 

19. 

2.85 

1.50 

20. 

5.02 

4.50 

21. 

.91 

3.00 

22. 

.79 

3.75 

23. 

G.01 

1.50 

24. 

7.11 

5.00 

25. 

3.95 

4.00 

26. 

2.01 

5.00 

27. 

0.79 

4.00 

28. 

7.04 

3.00 

29. 

8.31 

3.50 

30. 

2.98 

Amount 
Given 

$2.00 

10.00 
5.00 
4.00 
6.00 
5.00 
5.00 

10.00 
8.00 
5.00 

10.00 
7.00 
8.00 

10.00 
4.00 


HAM.    COM  PL.    A  KITH. 2 


18  FUNDAMENTAL   PROCESSES 

Written  Work 

1.  Chicago  is  468  miles,  by  rail,  west  of  Pittsburg,  and 
New  York  is  445  miles  east  of  Pittsburg.  What  is  the  rail- 
road distance  from  Chicago  to  New  York,  via  Pittsburg? 

2.  A  man  purchased  a  farm  for  $6500 ;  built  a  barn  on  it 
at  a  cost  of  $1980;  a  house  for  $1825;  and  spent  on  im- 
provements on  the  land,  $971.  What  was  the  cost  of  the 
farm  and  improvements  ? 

3.  The  area  in  square  miles  of  the  main  body  of  the 
United  States  is  3,088,519;  the  outlying  possessions  are 
Alaska,  590,884  square  miles;  Hawaii,  6449;  Porto  Rico, 
3435 ;  Philippines,  115,026 ;  other  outlying  possessions,  761 
square  miles.     Find  the  total  possessions  in  square  miles. 

4.  The  average  annual  production  of  corn  in  the  United 
States  for  a  number  of  years  was  $854,000,000;  of  hay, 
$467,000,000;  the  production  of  cotton,  $406,000,000;  of 
wheat,  $395,000,000;  and  of  oats,  $254,000,000.  Find  the 
total  average  annual  value  of  these  five  productions. 

5.  The  values  of  the  ten  leading  exports  of  the  United 
States  for  the  year  1906  were:  cotton,  $413,137,936;  meat  and 
dairy  products,  $208,586,501 ;  iron  and  steel  and  machinery, 
$172,555,588  ;  copper,  $90,773,151  ;  petroleum,  $85,738,866  ; 
wood,  $77,255,225;  flour,  $58,399,727  ;  corn,  $52,840,269; 
wheat,  $49,158,650  ;  livestock,  $45,614,748.  What  was  the 
value  of  all  these  products  ? 

6.  The  values  of  the  ten  leading  imports  for  the  same  year 
were:  silk  and  silk  manufactures,  $100,052,211;  raw  and 
manufactured  fibers,  $99,635,731 ;  hides,  $83,884,981 ;  sugar, 
$79,015,471;*  chemicals,  $78,647,978;  coffee,  $72,252,465; 
cotton  goods,  $68,911,371;  wool  including  woolen  goods, 
$61,040,335;  india  rubber,  $58,664,651;  jewelry,  $46,047,021. 
Find  the  value  of  all  these  imports. 


SUBTRACTION  19 

SUBTRACTION 

1.  Subtract  by  2's  from  97  to  1 ;  by  3's  from  75  to  9. 

2.  Subtract  by  4's  from  78  to  2 ;  by  6's  from  98  to  2. 

3.  Subtract  by  7's  from  101  to  3 ;  by  8's  from  106  to  2. 

Subtraction  is  the  process  of  finding  the  difference  between 
two  numbers,  or  of  taking  one  number  from  another. 
The  minuend  is  the  number  from  which  we  subtract. 
The  subtrahend  is  the  number  to  be  subtracted. 
The  difference,  or  remainder,  is  the  result  of  subtraction. 
The  difference  added  to  the  subtrahend  equals  the  minuend. 
The  sign  — ,  called  minus,  indicates  subtraction. 
Only  like  numbers  can  be  subtracted. 
Give  differences  at  sight : 


4. 

5. 

6. 

7. 

8. 

9. 

3-2 

12-7 

11-9 

10-4 

11-2 

14-3 

4-1 

9-4 

7-4 

19-3 

16-8 

13-9 

5-4 

9-8 

9-5 

17-9 

15-6 

16-7 

7-3 

11-4 

17-8 

11-3 

14-5 

15-7 

8-4 

9-7 

12-6 

12-9 

12-8 

13-8 

7-2 

5-1 

11-5 

16-9 

14-7 

18-9 

10.  Subtract   each   of   the   following    numbers   from    20 ; 
then,  from  30,  40,  etc. 

4      6      11      17      13      14      7      8      12      10     15     14     16 

11.  Subtract  each  of  the  following  numbers  from  100. 

40      70      60      25      45      75      44      64      84      37      57      68 

12.  Take  27  from  65,  thus 

Subtract  in  like  manner: 
13.    72        14.    84        15.    91 
48  36  45 


65-20  =  45;  45- 

7  =  38. 

16.    63        17.    48 

18.    82 

24               32 

59 

20 


FUNDAMENTAL   PROCESSES 


A  clerk's  sales  book  shows  the  following  sales  and  amount 
given  by  customers.     Give  differences  at  sight : 


Sales 

19. 

$1.55 

20. 

1.15 

21. 

3.17 

22. 

1.78 

23. 

3.15 

24. 

1.79 

25. 

2.34 

Amount 

GIVEN 

$2.00 
1.50 
4.00 
2.00 
3.50 
5.00 
3.00 


Sales 

26. 

$  .49 

27. 

1.23 

28. 

1.06 

29. 

2.14 

30. 

.99 

31. 

1.29 

32. 

.87 

Amount 
given 

$  2.00 
5.00 
2.00 
3.00 
2.00 
10.00 
5.00 


Written  Work 
1.    From  632  take  374. 

Minuend       632  =  500  +  120  +  12  =  5  hundreds,  12  tens,  12  ones 
Subtrahend  374  =  300  +    70  +    4  —  3  hundreds,    7  tens,    4  ones 
Difference     258  =  200  +    50  +    8  =  2  hundreds,    5  tens,    8  ones 
Since   4   ones  cannot   be.  taken  from  2  ones,  take  1  ten  =  10   ones, 
from  3  tens;    10  ones  +  2  ones  =  12   ones;    12  ones  —  4  ones  =  8   ones. 
Since  7  tens  cannot  be  taken  from  the  2  tens  remaining,  take  1  hun- 
dred =  10    tens,   from   the    6    hundreds;    10    tens  +  2    tens  =  12    tens; 
12  tens  —  7  tens  =  5  tens.     5  hundreds  —  3  hundreds  =  2  hundreds. 

Test.  —  374  +  258  =  632.  By  adding  the  difference  to 
the  subtrahend,  pupils  can  quickly  discern  whether  the 
answer  is  correct. 

Explain  the  steps  in  finding  each  remainder : 
2.    800        3.    9004        4.    9080        5.    7001        6.    9040 
594  7907  5987  4908  5879 


206      1097 

3093      2093      3161 

Subtract : 

7.  30984   8.  54009 

9.  81704  10.  41711  11.  50000 

24987     31047 

54270     39111     42001 

SUBTRACTION 


21 


The  following  methods  of  subtraction  are  also  convenient: 

I.    By  adding  (the  method  used  in  making  change). 

l.    From  842  take  385. 

Think:  AVhat  number  added  to  5  will  make  12? 
(7.)  Write  down  7;  carry  1  to  8  tens  in  minuend. 
What  number  added  to  9  (8  +  1)  will  make  14? 
(5.)  Write  down  5;  carry  1.  What  number  added  to 
4  (3  +  1)  will  make  8  ?     (4.)    Write  down  4. 


842 

385 
457 


II.   By  subtracting  from  10. 

2.    From  653  take  378. 

Borrow  10,  subtract  8,  and  add  3,  thus : 
10  —  8  in  subtrahend  =  2 ;  2  +  3  in  minuend  =  5. 
10  —  7  in  subtrahend  =  3  ;  3  +  4  (5  —  1)  in  minuend  =  7. 
5—3  =  2.     The    steps  in    the    general    method   of  sub- 
traction   are    borrow,   add,   subtract.      In   this   they   are 
borrow,  subtract,  add. 

Write,  subtract,  and  test  four  problems  in  3  minutes : 
85980  9.   1070.01  15.    590680         21.    6459871 

71409  340.97  289796  2987598 


753 

378 
275 


4. 

57004 
20098 

10. 
11. 
12. 

13. 
14. 

1590.10 
210.89 

16. 

17. 

18. 

19. 
20. 

998076 
433011 

22. 

23. 

24. 

25. 
26. 

5798371 
3099384 

5. 

39702 
21308 

1953.01 
391.54 

598801 
303397 

8342901 

5217809 

6. 

70001 
39005 

*  401.97 
207.58 

743019 
556601 

7654321 

3456780 

7. 

98235 
60104 

8701.49 
511.10 

831001 
397018 

6543903 

4239001 

8. 

80021 
51037 

*  800. 67 
610.34 

458995 
233450 

4932459 

2013307 

22  FUNDAMENTAL   PROCESSES 

PROBLEMS 

1.  The    minuend    is    6389,  and   the   difference   is    4360 
Find  the  subtrahend. 

2.  From  the  sum  of  3645  and  5796,  subtract  their  dif- 
ference. 

3.  In  1900  the  population  of  New  York  State  was 
7,268,894  ;  of  Pennsylvania,  6,302,115.  How  much  greater 
in  population  was  New  York  than  Pennsylvania? 

4.  In  1906  Iowa  raised  373,275,000  bushels  of  corn ;  Mis- 
souri, 228,522,500  bushels.  How  much  did  the  corn  crop  in 
Iowa  exceed  the  crop  in  Missouri  ? 

5.  A  and  B  together  owe  me  $7650;  B  owes  me  $4675. 
After  each  pays  me  -1*1600  on  account,  find  the  amount  each 
one  still  owes  me. 

6.  A  retail  merchant  bought  goods  to  the  amount  of 
61457.  After  selling  stock  from  these  goods  to  the  amount 
of  $975,  he  found  that  the  remainder  of  the  goods  unsold 
had  cost  him  6473.     How  much  had  he  gained  or  lost  ? 

7.  Mr.  Adams  bought  a  farm  for  $8670;  he  expended 
in  improvements  on  barn  and  house,  81790;  on  stock  and 
farming  utensils,  $2080.  How  much  more  did  he  pay  for 
the  farm  than  for  improvements,  live  stock,  and  utensils? 

8.  The  surface  of  the  earth  contains  196,907,000  square 
miles,  of  which  144,500,000  square  miles  are  water.  How 
much  of  the  surface  of  the  earth  is  land  ? 

9.  A  father  divided  623.675  among  his  sons,  giving 
to  James  66750  and  to  Henry  6  5000  less  than  the  part 
remaining  after  James  was  paid  ;  to  Frank  he  gave  the 
remainder.      How  much  did  each  receive  ? 


MULTIPLICATION 


23 


MULTIPLICATION 

1.  Count  to  72  by  2's;   by  3*s  ;  by  4's;  by  6's;  by  9's. 

2.  Count   backwards    from  48    by  2's;    by  3's;    by  4's; 
by  6's ;  by  8's. 

3.  Count  forwards  to  96  by  3's ;  by  4's  ;  by  6's. 

4.  Count  to  25  by  5's ;  to  60  by  4's ;  to  99  by  9's. 

5.  Build  the  multiplication  tables  by  addition,  thus : 

2 
2     2 
2     2     2  [2  times  2  =  4 

2     2     2  ;   then  write  it  in  this  form  •  3  times  2  =  6 

4  times  2  =  8 

6.  Drill  on  these  tables  until  pupils  thoroughly  know  them : 


1 

2 
3 

2's 

3's 

4's 

5's 

6's 

7's 

8's 

9's 

10' s  11' s 

12s 

4 
6 

6 
9 
12 

8 

12 

16 

20 

24 

10 

12 

14 
21 

16 
24 
32 
40 
48 
56 
64 
•72 
80 
88 
96 

18 

27 
36 
45 
54 
63 
72 
81 
90 
99 
108 

20 
30 
40 
50 

22 

24 

15 
20 

25 
30 
35 
40 
45 
50 

18 

33 

44 
55 

36 

48 

60 

72 

84 

96 

108 

120 

132 

144 

4 

8 

24 

30 

36 

42 

48 

54' 

60 

66 

72 

28 
35 
42 
49 
56 
63 
70 
77 
84 

5 

10 

15 

6 

12 

18 

60 

70 

80 

90 

100 

110 

66 

77 

8* 

00 

110 

121 

7 

14 

21 

28 
32 
36 

8 

10 

24 

27 

9 

18 

10 

20 

as 

40 

11 

22 

44 

55 
60 

12 

24 

36 

IS 

120  132 

The  fust  row  of  figures  at  the  top  stands  for  the  different  tables.  By 
multiplying  each  of  the  numbers  in  the  first  left-hand  row  by  each  of  the 
numbers  in  the  top  row,  the  tables  can  all  be  made.  Thus,  in  the  table 
of  the  twos,  the  products  are  directly  below  the  number  of  the  table,  etc. 


24  FUNDAMENTAL   PROCESSES 

7.  How  many  units  are  there  in  4?  4x15  means  that  we 
are  to  take  $5,  four  times  to  find  the  product;  this  may  be 
found  in  two  ways  :  $5  +  $5  +  $5  +  #5  =  $20,  orby  multipli- 
cation, which  is  a  short  form  of  addition ;  thus,  4  x  §5  =  $20. 

Multiplication  is  the  process  of  taking  one  number  as  many 
times  as  there  are  units  in  another  number. 

The  multiplicand  is  the  number  multiplied. 

The  multiplier  is  the  number  by  which  we  multiply. 

The  product  is  the  result  of  multiplication. 

The  sign  x  indicates  multiplication ;  it  is  read,  "  times," 
when  the  multiplier  precedes  the  sign,  and,  "  multiplied  by," 
when  the  multiplier  follows  the  sign. 

Read  each  statement  and  then  give  products. 

8.  4x$12  10.    12  x  7  yards         12.    11  x  4  pounds 

9.  9  x  6  horses         11.      5x8  ft.  13.      7x8  bushels 

14.  In  the  above  statements,  how  many  times  are  $12 
taken?  8  bushels?  7  yards? 

15.  Name  the  multiplicands  in  the  above  statements ;  the 
multipliers. 

A  concrete  number  is  a  number  used  with  reference  to  a 
particular  object  ;  as,  5  days,  10  pounds,  8  inches. 

An  abstract  number  is  a  number  used  without  reference  to 
a  particular  object ;  as,  5,  8,  20. 

Name  the  abstract  and  the  concrete  numbers  in  the  follow- 
ing statements  and  then  give  products : 

16.  12  x  7  days  18.    11  x  $7  20.      6  x  11 

17.  15x10  19.      9  x  12  ft.  21.    12x5^ 
The  multiplier  is  always  regarded  as  an  abstract  number.    The 

multiplicand  may  be  either  abstract  or  concrete. 

22.  In  problems  16-21  are  the  products  like  the  multipli- 
cand or  the  multiplier  ? 

The  product  and  the  multiplicand  are  like  numbers. 


MULTIPLICATION  25 

Oral  and  Written  Analysis 

1.  How  many  eggs  are  there  in  6  dozen? 
Since  there  are  12  eggs  in  one  dozen,         1  doz.  =  12  eggs; 

in  6  doz.  there  are  6  x  12  eggs=72  eggs.         6  doz.  =  6x  12  eggs=72  eggs. 

2.  How  many  trees  are  there  in  an  orchard  if  then;  are 
11  rows  and  10  trees  in  each  row  ? 

3.  James  raised  7  bushels  of  potatoes  on  an  average  from 
each  of  10  rows.     How  many  bushels  did  he  raise? 

What  is  the  cost  of : 

4.  10  quarts  of  cherries  at  8^  per  quart? 

5.  9  quarts  of  milk  at  7^  per  quart? 

6.  8  bushels  of  apples  at  $2  per  bushel? 

7.  A  twelve-pound  cheese  at  12^  per  pound? 

8.  3  pecks  of  apples  at  25^  per  peck? 

9.  How  far  does  a  boy  ride  on  his  automobile  in  4  hours 
at  the  rate  of  9  miles  per  hour? 

10.  How  many  miles  are  there  in  4  streets,  if  the  streets 
average  12  miles  ? 

11.  There  are  32  quarts  in  a  bushel.     Find  the  number 
of  quarts  in  13  bushels. 

12.  How  far  does   an   automobile  run   in  4   hours,  if   it 
averages  14  miles  per  hour? 

13.  Find  the  cost  of  posting  18  letters  at  2^  each. 

14.  Find  the  cost  of  a  7-pound  turkey  at  13^  per  pound. 

15.  A  lady  purchased  2  dozen  oranges  at  40^  per  dozen. 
How  much  did  they  cost? 

16.  It  takes   John  15  minutes  to  walk  to  school.     How 
many  minutes  will  be  required  to  walk  to  school  60  times? 

17.  Frank  used  12  tablets,  at  10^  each,  in  a  school  term. 
How  much  did  they  cost? 


26  FUNDAMENTAL    PROCESSES 

Written  Work 

1.    Multiply  146  by  3. 

Multiplicand  146  3x6  ones  =  18  ones,  or  1  ten  and  8 

Multiplier              3  ones.     Write  8  in  ones'  place  and 

Product             438  carry  the  1  ten.     3x4tens  =  12  tens ; 

„              +.n      -  .  n.      -.~  .  ~~       12  ten  s+ the  1  ten,  carried  from  ones' 

Test.-146  +  14b  +  146  =  438      place  =  13  tenB,or  j  himdred  and  3 

tens.    Write  3  in  tens'  place  and  carry  the  1  hundred.     3x1  hundred  =  3 
hundreds ;  3  hundreds  +  the  1  hundred  =  4  hundreds.     The  product  is  438. 

Find  products  : 

2.    139       6.    674     10.    307     14.    137      18.    427     22.    507 

3  3  5  6  7  6 


- 



3.    135 

7.    278 

li.    342 

15. 

673 

19.    784 

23.     196 

_2 

J 

6 

5 

7 

8 

4.    603 

8.    147 

12.    281 

16. 

901 

20.    249 

24.    379 

4 

5 

4 

7 

8 

7 

5.    205 

9.    219 

13.    309 

17. 

419 

21.    907 

25.    583 

2 

4 

_6 

_6 

2 

_8 

26.    Multiply  $1.25  by  3. 

$1.25 
3 

Place  the  decimal 
under  the  decimal  poir 

point  in  the  product  directly 
it  in  the  multiplicand. 

$3.75 

27.    $2.53     30.    $8.09     33.    $3.27     36.    $2.41     39.    $3.19 
9  9  8  10  9 


28.  $6.08  31.    $2.25  34.    $1.04  37.    $3.74  40.    $8.92 
_9             10             11             12  10 

29.  $9.09  32.    $1.29  35.    $3.05  38.    $5.05  41.    $9.08 

9  11  10  12  12 


Ul'LTIl'LK  ATIOX 


27 


Multiplication  by  Larger  Numbers 

Multiplying  integers  by  20.  100.  1000.  etc. 
lnx12=12<);  100x2=200;   1000x2  =  2000. 

Any  integer  may  he  multiplied  by  10,  100,  1000,  etc.,  by  an- 
nexing to  the  integer  as  many  naughts  as  there  are  naughts  in 
the  multiplier. 

Multiply  each  number  by  10,  by  100,  by  1000,  writing 
only  the  products :  16,  409,  290,  301,  205,  250,  175,  791. 


Written  Work 

l.    Multiply  72 

by 

36. 

Multiplicand 

72 

72           In   practice, 

Multiplier 

36 

qq      the   0    in    the 

1                 l  *      1 

1st  partial  product 
2d  partial  product 

432  = 
2160  = 

6  x72 
30  x  72 

.on       second  partial 

product      is 

-jXU         omitted,     and 

Entire  product 

2592  = 

36  x  72 

2592      21  (JO  is  written 
as  216  tens. 

Find  products : 

2.    150  x  40 

4.    805 

xl6 

6.    304  x  71 

3.    107  x  35 

5.    500 

x70 

7.    691  x  74 

Multiply  and  test : 

8.    6425 

■  a. 

245 

Form  100  problems  by  mul- 

9.   1024 

b. 

344 

tiplying  each  multiplicand  by 

10.    8720 

0. 

564 

each  of  the  multipliers,  thus: 

n.    9652 

d. 

746 

8  a. 

245  x  6425  =  ? 

12.   m\o 

.    by    . 

e. 

804 

8  5. 

344  x  6425  =  ? 

13.    7894 

/■ 

961 

15  i. 

968  x  7695  =  ? 

14.    8465 

9- 

869- 

Write,  solve,  and  test  each 

15.  7695 

16.  8425 

h. 
i. 

796 
968 

problem  in  1|  minutes. 

17.    9476, 

■J- 

898 

28  FUNDAMENTAL   PROCESSES 

18  How  much  will  20,000  bricks  cost  at  $7.75  per  thou- 
sand ? 

Suggestion :  20,000  =  20  thousand  =  20  M. 

19.  A  ranchman  sold  125  head  of  cattle  at  an  average  of 
$42.75  per  head,  and  625  sheep  at  $3.85  per  head.  Find 
the  total  amount  of  his  sales. 

20.  The  cost  of  drilling  an  oil  well  was  35/  per  foot  for 
drilling  and  65^  for  the  tubing.  If  the  well  was  drilled 
1177  feet  and  tubed  700  feet,  find  the  total  cost. 

21.  The  freight  rate  on  corn  in  car-load  lots  from  Omaha, 
Neb.,  to  New  York  City  is  20^  per  hundred  pounds.  Find 
the  freight  on  a  car  of  42,000  lb. 

22.  A  freight  train  of  32  cars  is  laden  with  corn.  The 
cars  contain  an  average  of  700  bushels  of  56  lb.  each.  Find 
the  weight  of  the  corn  in  pounds. 

23.  A  commission  merchant  sold  1275  barrels  of  apples  at 
the  rate  of  $3.25  per  barrel,  charging  $.325  per  barrel  for 
selling.  How  much  was  realized  from  the  sale  of  the  apples 
after  the  charges  for  selling  were  deducted? 

24.  A  man  owned  a  farm  of  142  acres,  worth  $72.50  per 
acre  ;  5  city  lots  worth  $  1875  per  lot ;  and  a  business  house 
worth  $6350.     Find  the  value  of  his  entire  property. 

25.  Frank  lives  87  rods  from  the  schoolhouse.  How 
many  rods  does  he  walk  in  going  to  school  140  days,  if  he 
returns  home  each  day  for  his  dinner  ? 

26.  Two  trains  leave  a  station  at  the  same  time.  One 
travels  west  38  miles  per  hour  ;  the  other  travels  east  45  miles 
per  hour.     How  far  apart  are  they  in  9  hours  ? 

27.  A  dealer  bought  a  car  load  of  coal,  42,000  lb.,  at  $1.90 
per  ton  of  2000  lb.  If  the  freight  was  70^  a  ton,  and  he 
retailed  the  coal  at  $3.25  a  ton,  find  his  profit. 


DIVISION  29 

DIVISION 

1.  How  many  times  is   the  number  6  contained  in  24? 
Division  is    the  process  of    finding   how  many  times  one 

number  is  contained  in  another,  or  of  separating  a  number 
into  equal  parts. 

The  dividend  is  the  number  to  be  divided. 

The  divisor  is  the  number  by  which  we  divide. 

The  quotient  is  the  result  of  division. 

The  remainder  is  the  part  of  the  dividend  remaining  when 
the  quotient  is  not  exact. 

The  sign  +  indicates  division,  and  is  read,  "  divided  by." 

Give  quotients : 

24  +  6  84  +  7  64  +  8  49  +  7  99  +  11 

72  +  9  108  +  9  42  +  6  68  +  9  72+12 

81  +  9  72+8  90  +  9  96  +  8  77  +  11 

Division  is  indicated  in  three  ways  :   14  +  2;   2)14;   and-M-. 
How  many  times  are  : 

2.  2  inches  contained  in  (may  be  taken  from)  12  inches? 

3.  4  yards  contained  in  (may  be  taken  from)  12  yards? 

If  both  the  dividend  and  divisor  are  concrete,  they  must  be 
like  numbers. 

Compare  18  +  2  with  J  of  18 ;  15  +  3  with  }  of  15. 
How  many : 

4.  Cents  are  |  of  48  f  ?     48^+8=— cents. 

5.  Cents  does  one  orange  cost  if  4  oranges  cost  20^? 

In  separating  a  number  into  equal  parts,  the  divisor  is  always 
an  abstract  number  and  the  quotient  is  like  the  dividend. 

This  kind  of  division  is  called  partition. 

In  the  following,  point  out  the  problems  in  partition  : 

6.  $120  +  10  7.    \  of  40^  s.    24  ft. +2  ft. 


30 


FUNDAMENTAL   PROCESSES 


Remainder  in  Division 

34-r-5  =  6,  and  4  remaining.     $39  -4-  5  =  $7,  and  $4  re- 
maining. 

Give  quotients  and  remainders  : 

$26 -=-6;    79 -h  8;    $48  -4- $9;  37-*-  4;    84^-*- 8^;    49-4-7. 


Written  Work 


l.    Divide  236  by  3. 
Divisor  3)236  Dividend 


78  Quotient 
Remainder  2 
Test.  —  3  x  78  =  234 ; 
234  +  2  =  236 


23  tens  -=-3  =  7  tens,  and  2  tens 
(20  ones)  remaining.  Write  the  7 
in  tens'  place. 

20  ones  +  6  ones  =  26  ones ;  26  ones 
-4-3  =  8  ones,  and  2  ones  remaining. 
Quotient  78;  remainder  2. 
We  think:  "3  in  23,  7  times,  and  2  remaining;  3  in  26,  8  times,  and 
2  remaining." 

Find  quotients : 

2.   344  -*-  3  3.   763  ft.  -4-  6  ft.  4.  466  i  -4-  9 

Divide  $6.48  by  3. 

3)$  6.48  Place  the  decimal  point  in  the  quotient  directly 

$2.16  under  the  decimal  point  in  the  dividend. 


Divide  and  test : 


5. 
6. 
7. 

8. 

9. 
10. 
11. 
12. 
13. 
14. 


$203,751 

$678.34 

$209.07 

$390.08 

$720.93 

$379.38 

$297.34 

$427.84 

$918.07 

$847.12 


by 


a. 

2 

b. 

3 

c. 

4 

d. 

5 

e. 

6 

/• 

7 

9- 

8 

L 

9 

i. 

10 

• 

11 

Form  100  problems  by  divid- 
ing each  dividend  by  each  of 
the  divisors,  thus  : 

5  a.  $203.75 -f- 2=  ? 
5  6.  $203.75-*- 3  =  ? 
9e.  $720,934-6  =  ? 

Write,  solve,  and  test  two 
problems  in  1  minute. 


LONG    DIVISION  31 

Dividing  by  Larger  Numbers 

1.  Divide  50,  90.  150,  600,  1 by  10. 

2.  Name  the  quotients  when  130,  170,  1200,  2000,  100,  is 
each  divided  by  10. 

3.  Divide  500,  600,  1500,  and  2500  by  100. 

Removing  one  naught  from  the  right  of. a  number  divides  the 
number  by  10  ;  removing  two  naughts,  divides  it  by  100;  remov- 
ing three  naughts  divides  it  by  1000 ;  etc. 

4.  Divide  225  by  20,  thus :  2 1 0)22  '5         o  tens  js  contained  in 

1115       22  tens  11  times,  with  5 
20    remaining.    5  -=-  20  =  5%. 

5.  Divide  2375  by  20  ;  by  200. 

Divide  each  number  by  20  ;  by  50  ;   by  80  ;   by  500. 

6.  37,845.       8.    90.200       10.    409,805.        12.    390,075. 

7.  50,240.        9.    74,079       11.    790,086.        13.    985,000. 

LONG   DIVISION 

1.  Divide  4310  by  21.  Steps 

205  1.   Divide  43  by  21.     Write  the  quotient 

91  VPvFT)  figure  2  over  the  figure  3  of  the  dividend. 

'  2.    Multiply  21  by  2. 

_ 3.   Subtract  42  from  13. 

HO  4.    Bring  down  the  next  figure.       Is  21 

105  contained  an  integral  number  of   times  in 
5  remainder      H?     Write  O  in  the  quotient. 

Test:  21  x  205  =  4305      5>  BrinS  dowu  the  next  fiSure  and  Pro" 

,"      _  '*  -        ,01  n         ceed  as  before.     Write  5  in  the  quotient. 

4305  +  o  =  4310 

Divide  and  test : 

2.  252-21  7.  2214 -s- 21  12.  1326-*- 51 

3.  525 -j- 21  8.  4601-4-22  13.  1922-62 

4.  724-22  9.  1271-f-31  14.  2193-5-51 

5.  642-31  10.  1344-42  is.  7010-4-91 

6.  345-4-31  11.  1024-*- 32  16.  6874-81 


32 


FUNDAMENTAL   PROCESSES 


Divide  and  test 


17. 

1364  by  i 

>2 

25.    6207  by  76 

33. 

8538  by  94 

18. 

1395  by  31 

26.    6572  by  68 

34. 

7646  by  87 

19. 

1728  by  42 

27.    7010  by  91 

35. 

8544  by  79 

20. 

2193  by  51 

28.    7284  by  92 

36. 

9584  by  m 

21. 

2583  by  63 

29.    6874  by  81 

37. 

7001  by  84 

22. 

3034  by  74 

30.    6986  by  83 

38. 

8200  by  77 

23. 

4345  by  65 

31.    7044  by  86 

39. 

7909  by  96 

24. 

5072  by  59 

32.    8406  by  92 

40. 

8549  by  78 

41. 

1009 

42 

$11.17 

715)* 7986. 55 

43. 

544 

395)398555 

805)437920 

395 

715 

4025 

3555 

836 

3542 

3555 

715 
1215 

3220 
3220 

Since   35  does  not  coi 

itain           715 

3220 

395,   the   second  figure   in 

the         5005 

quotient  is  0. 

5005 

Divide  and  test : 

44. 

6464341 

'  a.    268        Form 

100  problems  by  di- 

45. 

7846760 

b.    354    viding  each  dividend  by  each 

46. 

5864548 

c.    676    of  the  divisors,  thus  : 

47. 

8645341 

d.    758      44  a.    1 

3464341 

-h  268  =  ? 

48. 

9624872 

1 

e.   865      44  b.    I 

3464341 

-f-  354  =  ? 

49. 

7784100 

■    by    ■ 

/.    984      49  c.    ' 

r784100 

-676  =  ? 

50. 

6810404 

g.    789        Write 

',  solve,  and  test  each 

51. 

7904025 

A.    897    problem 

in  2  minutes. 

52. 

4867045 

i.   509 

53. 

3234567 

J.   890 

MULTIPLICATION    AND    DIVISION  33 

Problems  of  Two  or  More  Operations 

1.  If  48  barrels  of  flour  cost  $324,  how  much  will  275 
barrels  cost? 

Cost  of  4S  bbl.  =  $  324.00  Study  of  Problem 

Cost  of  lbbL  =  1824.00 -«-48  =  * 6.75  i.   What   is  given    in 

Cost  of  275  bbl.  =  275  x  $6.75  =  $1856.25      this  problem? 
a.   Number  of  barrels  in  each  purchase,      b.    Cost  of  48  bbl. 

2.  What  is  required?     a.   Cost  of  1  bbl.      b.   Cost  of  275  bbl. 

3.  How  do  you  find  what  is  required?  a.  Divide  cost  of  first  pur- 
chase by  the  number  of  barrels,  b.  Multiply  the  cost  of  1  bbl.  by  the 
number  of  barrels  purchased. 

Note.  —  The  purpose  of  these  studies  is  threefold  : 

1.  To  train  the  pupil  to  see  and  understand  the  conditions  of  a  problem. 

2.  To  give  that  logical,  analytic  grasp  of  conditions  that  forms  the 
basis  of  all  mathematical  power. 

3.  To  direct  the  teacher  in  his  efforts  to  attain  these  ends. 

2.  If  2675  bushels  of  wheat  cost  $2728.50,  how  much  are 
196  bushels  worth? 

3.  A  water  tank  holds  8640  gallons.  If  it  receives  728 
gallons  per  hour  by  one  pipe  and  discharges  512  gallons  by 
another,  in  what  time  will  it  be  filled  ? 

4.  Two  steamers  sail  towards  each  other  from  opposite 
sides  of  the  Pacific  Ocean.  If  the  distance  across  is  9872 
miles,  and  one  sails  at  the  rate  of  285  miles  a  day,  and  the 
other  332  miles  per  day,  in  how  many  days  will  they  meet  ? 

5.  The  daily  pay  of  a  railway  conductor  is  $3.45.  If  he 
works  310  days  in  a  year,  and  spends  on  an  average  $65 
per  month,  how  much  has  he  left  at  the  end  of  the  year? 

6.  The  receipts  of  a  street  railway  for  365  days  were 
$119,685.23.  Find  the  average  daily  profits  if  the  total 
expenses  were  $96,478.02. 

7.  A  and  B  divide  an  estate  of  $9875  between  them.  If 
A  receives  $275  more  than  B,  how  much  does  each  receive? 


34  FUNDAMENTAL   PROCESSES 

8.  A  man  sold  128  acres  of  land  at  #70  an  acre,  and  96 
at  $90  an  acre.  He  invested  the  money  in  town  lots  at  $550 
each.     How  many  did  he  buy  ? 

Study  of  Problem 

1.   What  is  given  in  the  problem? 
$8960  value  of  1st  farm  2    What  is  required? 

$8640  value  of  2d  farm  3.    What  is  the  first  step  in  the 

$17600  value  of  both  solution?     the  second?     the  third? 

the  fourth? 

$17600  -r-$  550  =  32,  no.  of  lots  bought. 

9.  If  it  costs  40  cents  to  ship  a  10-gallon  can  of  milk 
from  Hickory  to  Pittsburg,  how  much  does  the  railroad 
realize  in  5  days,  from  a  shipment  of  135  cans  per  day? 

10.  A  shipper  pays  20  cents  per  barrel,  per  month,  cold 
storage  charges  on  apples,  and  15  cents  per  firkin  on  butter. 
Find  the  charges  for  three  months  on  45  firkins  of  butter 
and  328  barrels  of  apples. 

11.  A  locomotive  in  making  a  certain  trip  uses  18  tons  of 
coal.  If  a  trip  is  made  in  2  days,  how  much  coal  will  the 
engine  consume  in  190  days? 

12.  A  dealer  buys  three  boxes  of  oranges  for  $3.50,  $2.75, 
and  $2.50,  respectively.  If  he  sells  10  dozen  at  50  cents  per 
dozen,  9  dozen  at  40  cents  per  dozen,  12  dozen  at  35  cents 
per  dozen,  and  the  remaining  5  dozen  at  25  cents  per  dozen, 
find  his  gain. 

13.  An  opera  sale  of  tickets  is  as  follows:  450  @  $1.50; 
380  @  $1.00;  520@$.75;  310@$.50;  and  240  @  $.25. 
Find  the  total  sale  of  the  tickets,  and  the  average  cost  of 
each  ticket. 

14.  A  steamboat  consumes  23  tons  of  coal  per  day.  Find 
the  cost  of  the  coal,  at  $5.85  per  ton,  for  a  trip  of  39  days. 


COMPARISON 

COMPARISON 

Comparison,  as  here  used,  indicates  the  relation  of  two  simi- 
lar numbers,  expressed  by  the  quotient  of  the  first  number 
divided  by  the  second. 

1.  Compare  10  and  5;  12  and  4;  16  and  8;  20  and  5; 
24  and  6. 

2.  20  is  how  many  times  4?  30  is  how  many  times  6? 
How  does  40  compare  with  4? 

3.  What  is  the  quotient  of  48  divided  by  8?  by  6?  by  4? 

4.  Compare  200  and  50;  400  and  100;  500  and  250. 

5.  125  is  what  part  of  250?     of  500?     of  375?     of  625? 

6.  Compare  48  feet  and  2  yards:    75  feet  and  5  yards. 
Xote.  —  Change  yards  to  feet,  or  feet  to  yards ;  then  compare. 

7.  6  feet  is  what  part  of  3  yards?     of  10  yards? 

Written  Work 

1.  When  4  pounds  of  butter  cost  80  cents,  how  much  will 

12  pounds  cost? 

Xote.  — 12  pounds  =  3x4  pounds:  hence,  12  pounds  will  cost  3  x  80 
cents. 

2.  Find  the  cost  of  10  barrels  of  apples,  when  2  barrels 

cost  64.50. 

3.  At  3  pounds  of  coffee  for  $1,  how  much  will  15 
pounds  cost  ? 

4.  How  much  will  30  yards  of  silk  cost  when  3  yards 
cost  63.75? 

5.  When  2  doz.  oranges  are  selling  for  60  cents,  how 
much  will  8  dozen  cost? 

6.  Find  the  cost  of  20  barrels  of  cement,  when  5  barrels 
cost  66.25. 

7.  How  much  will  ••'><>  dozen  eggs  cost,  when  •*•  dozen  sell 
for  si? 


36  FUNDAMENTAL   PROCESSES 

COMBINING    PROCESSES 

A  parenthesis  (  )  or  a  vinculum  '  "  groups  together 

several  numbers  and  shows  that  the  operations  within  the 
groups  are  to  be  performed  first ;  thus,  6  —  (3+  2)  =  6  —  5  =  1 ; 
(5  + 3)  x  2=  8x2=  16;  5  +  (3x2)  =  5  +  6=ll;  32-^4  +  3 
=  8  +  3  =  11;  4x2-3=8-3  =  5. 

When  no  parenthesis  or  vinculum  is  used,  the  signs  x  and 
-=-  indicate  operations  that  are  to  be  performed  before  those 
indicated  by  either  +  or  -  ;  thus,  4  +  8  x  3  =  4  +  (8  x  3),  or 
28 ;  5  +  12  -=-  6  =  5  +  (12  -*-  6),  or  7. 

In  an  expression  like  12  -s-  6  x  2,  mathematicians  are  not 
agreed  as  to  which  sign  shall  be  used  first.  To  avoid  ambi- 
guity, the  parenthesis  should  be  used  in  such  expressions. 
Thus,  (12  -s-  6)  x  2  =4  ;  but  12  +  (6  x  2)  =  1. 

Find  the  value  of : 

!.   4  x  12  -  16  +  4.  5.  (240  +  98)  x  (688  -  425). 

2.7  +  8x7-26.  6.  (56-18)  x  11  +  4-6  x  4. 

3.  (14  +  8  -  6)  x  9.  7.  (84  -  7  x  6  +  9  x  4  -  6)  +  9. 

4.  (87-65  +  96)  x  24.    8.  (56  +  7)  x  12  +  97-7  x  9. 
9.    6+10x5  +  8  +  2-4-2  +  8. 


10.  7  x  5~+4  +  8^T6  +  2  -  3  x  4. 

11.  (6-+  2  x  3)  +  4  +  (3  x  6)  +  2  +  2  x  (3  +  5  -  2). 

12.  36- 6x4  +  2x6+ (40 +  5) +9  + 3x6. 

13.  10  +  20-5  x  3  +  6x2-=-  3  +  5x6. 

14.  3x(4+5-2)  +  4+5x(4x5  +  2)+5. 

15.  3  x  (6  +  8)  +  7  x  (8  +  2)  -  3  x  (6  +  3)  +  15  -  7. 

16.  175  -  8  x  (19  -  10)  -  25  -*-  5  +  6^7  -9  +  3. 


FACTORS   AND   DIVISORS 

1.  What  two  numbers  will  give  6  as  a  product?  8  as  a 
product?    10  as  a  product? 

2.  What  are  2  and  3  in  relation  to  6?  4  and  2  in  relation 
to  8?   5  and  2  in  relation  to  10? 

An  integer  or  an  integral  number  is  a  whole  number. 
The  factors  of  a  number  are  the  integers  whose  product  is 
the  number  ;  thus,  5  and  2  are  factors  of  10. 

3.  Name  two  factors  that  produce  24,  32,  40,  56,  49,  72,  96. 

A  factor  of  a  number  is  an  exact  divisor  of  the  number  ; 
that  is,  it  is  contained  in  the  number  an  integral  it  umber  of 
times. 

4.  Name  the  exact  divisors  of  54,  81,  48,  36,  66,  64,  63. 

2  x2  =  4 

5.  Observe  the  two  equal  factors  that  pro-    3  x  8  _  9 

duce  4;   9;  16.  4  x  4  =  10 

2x2x2=8 

6.  Observe  the  three  equal  factors  that  pro-    3  x  3  x  3  =  27 

duce  8  ;  27  ;  64.  4  x  4  x  4  =  64 

Instead  of  repeating  a  factor,  a  small  figure  called  an 
exponent  may  be  written  to  the  right  and  a  little  above  the 
number  to  show  how  often  it  is  used  as  a  factor  ;  thus, 
33  =3x3x3  =  27:  24  =2x2x2x2  =  16. 

7.  What  number  will  divide  9  and  10?    21  and  25? 

Numbers  are  prime  to  each  other  when  they  have  no  com- 
mon factor  ;   thus,  9  and  10  are  prime  to  each  other. 

37 


38  FACTORS  AND  DIVISORS 

Even  numbers  are  numbers  that  contain  the  factor  2. 

Odd  numbers  are  numbers  that  do  not  contain  the  factor  2. 

8.  What  are  the  factors  of  7?  of  11?  Observe  that  7 
and  11  have  no  exact  divisors  except  themselves  and  one. 

A  prime  number  is  one  that  has  no  exact  divisor  except 
itself  and  one  ;  thus,  5,  2,  and  3  are  prime  numbers. 

9.  Name  all  the  prime  numbers  to  31. 

10.  What  are  the  factors  of  15?  Observe  that  15  can  be 
divided  by  3  and  5.  It  is  composed  of  other  factors  than 
itself  and  one. 

A  composite  number  is  one  that  has  other  exact  divisors 
than  itself  and  one ;  thus,  6  and  10  are  composite  numbers. 

11.  Name  all  the  composite  numbers  to  50. 

TESTS  OF  DIVISIBILITY 

1.  Divide  12,  24,  26,  38,  and  50  each  by  2.  What  is  the 
ones'  figure  in  each  of  the  dividends?  Divide  other  num- 
bers ending  in  2,  4,  6,  8,  or  0  by  2. 

A  number  is  divisible  by  2,  if  the  ones'1  figure  is  2,  4,  6,  8, 
or  0. 

2.  Divide  15,  25,  40,  125,  150  each  by  5.  What  is  the 
ones'  figure  in  each  dividend?  Divide  other  numbers  end- 
ing in  5  or  0  by  5. 

A  number  is  divisible  by  5,  if  its  ones'  figure  is  5  or  0. 

3.  Divide  36,  69,  48,  72,  162,  369  each  by  3.  Notice 
that  the  sum  of  the  digits  (that  is,  of  the  figures)  in  each 
number  is  divisible  by  3.  Divide  by  3,  other  numbers  the 
sum  of  whose  digits  is  divisible  by  3. 

A  number  is  divisible  by  3,  if  the  sum  of  its  digits  is  divis- 
ible by  3. 


FACTORING  39 

4.  Divide  18,  27,  279,  819,  639  each  by  9.  Notice  that 
the  sum  of  the  digits  in  each  dividend  is  divisible  by  9. 
Divide  by  9,  other  numbers  the  sum  of  whose  digits  is  divis- 
ible by  9. 

A  number  is  divisible  by  9,  if  the  sum  of  its  digits  is  divisible 
by  9. 

5.  Select  the  numbers  that  are  divisible  by  2  ;  by  3 ;  by 
5 ;  by  9. 

86        96        123        918        515        3672 

94        72        321         819        450         1909 

FACTORING 

1.  Give  the  two  factors  that  produce  15. 

2.  If  one  of  them  is  given,  how  may  the  other  be  found  ? 

To  separate  a  number  into  two  factors,  take  any  exact  divisor 
for  one  factor  and  the  quotient  of  the  number  by  this  factor  for 
the  other. 

Factoring  is  the  process  of  separating  a  number  into  its 
factors. 

A  prime  factor  is  a  prime  number  used  as  a  factor ;  thus, 
3  and  5  are  the  prime  factors  of  15. 

Written  Work 
1.    Find  the  prime  factors  of  126. 

Divide   by  the   least   prime   factor ; 
divide  the  quotient  by  the  next  smallest 
prime  factor,  etc..  until  the  last  quotienl 
is  a  prime  number.     The  divisors  and 
_  0      o      o      "_io£    the  last  quotient  are  the  prime  factors; 

thus,  2,  3,  3,  and  4   are  the  prime  fac- 
0*i  tors  of  126. 

2  x32x  7  =  l:2i; 


2 
3 
3 

126 
63 
21 

40  FACTORS   AND   DIVISORS 

Find  the  prime  factors  of : 


2. 

125 

6. 

945 

10. 

2431 

14. 

25600 

3. 

210 

7. 

2934 

li. 

7200 

15. 

64640 

4. 

225 

8. 

4620 

12. 

7700 

16. 

97125 

5. 

400 

9. 

3822 

13. 

6525 

17. 

78000 

GREATEST  COMMON  DIVISOR 

1.  Name  a  number  that  will  exactly  divide  both  16  and 
24 ;  15  and  25 ;  14  and  27. 

A  common  divisor  of  two  or  more  numbers  is  a  number 
that  exactly  divides  each  of  them ;  thus,  4  is  a  common 
divisor  of  16  and  24. 

2.  Is  4  the  greatest  number  that  will  exactly  divide  16 
and  24?  What  is  the  greatest  number  that  will  exactly 
divide  16  and  24  ? 

The  greatest  common  divisor  (g.  c.d.)  of  two  or  more 
numbers  is  the  greatest  number  that  exactly  divides  each 
of  them;  thus,  9  is  the  g.c.d.  of  27  and  36. 

3.  Name  the  g.  c.  d.  of  24  and  36 ;  of  32  and  40. 

Written  Work 
l.    Find  the  greatest  common  divisor  of  56,  98,  154. 

56      98      154  As  the  g.c.d.  of  two   or  more   numbers   is  the 

28  4^>  77  product  of  all  their  common  prime  factors,  divide 
the  numbers  by  their  common  prime  factors. 
In  the  same  way  divide  the  quotients  until 
they  are  prime  to  each  other.  The  divisors 
2  and  7  are  all  the  common  prime  factors  of  the 
numbers.  Hence,  the  g.c.d.  of  56,  98,  and  154 
is  2  x  7,  or  14. 


2 
7 


4       7       11 
g.  c.  d=2  x7,  or  14. 


LEAST    COMMON    MULTIPLE  41 

Find  the  p-.c.d.  of: 

2.  42,  63,  189  7.  84,  56,  210 

3.  54,  216,  360  8.  22,  110,  132 

4.  48,  60,  96  9.  42,  84,  175 

5.  84,  252,  512  10.  17,  68,  85 

6.  21,  48,  78  11.  432,  720,  864 

LEAST  COMMON   MULTIPLE 

1.  Name  a  number  that  will  exactly  contain  6  and  9 ;  8 
and  12;   7  and  9. 

A  common  multiple  of  two  or  more  numbers  is  a  number 
that  is  exactly  divisible  by  each  of  them ;  thus,  36  is  a  com- 
mon multiple  of  6  and  9. 

2.  Name  the  least  number  that  is  exactly  divisible  by  6 
and  9;  hy  8  and  12. 

The  least  common  multiple  (l.c.m.)  of  two  or  more  num- 
bers is  the  least  number  that  is  exactly  divisible  by  each  of 
them ;  thus,  18  is  the  1.  c.  m.  of  6  and  9. 

3.  Name  the  1.  c.  i».  of  6  and  8  ;  of  9  and  12  ;  of  8  and  12. 

Written  Work 

l.    Find  the  1.  cm.  of  18,  32,  and  40. 

18  =  2x3x3  The  I.  c.  m.  of  two  or  more  numbers  is 

QO_  O  y  •)  x  O  x  9  x  9  the  product  of  all    their    prime  factors, 

tn     \      r.      -^      r  each  factor  being   used  as   often   as  it 

40  =    x    x  2  x  5 

occurs  in  any  number. 

1.  c.  m.  =  i5  x  o2  X  5,  or  1440.  o  occurs  5  times  as  a  factor  in  32. 
It  must,  therefore,  be  used  5  times  in  the  1.  cm.  3  occurs  twice  as  a 
factor  in  18;  it  must,  therefore,  be  used  twice  in  the  1.  c.  m.  5  occurs 
once  as  a  factor  in  1<>;  it  must,  therefore,  be  used  once  in  the  1.  c.  m. 
Hence, the  1.  c.  111.  of  is,  32,  and   ID  is  L)5  x  32X  5  =  1110. 


42  FACTORS   AND   DIVISORS 

2.    Find  the  ].  c.  m.  of  12,  36,  54,  and  63. 

'**  —  -  Since  12  is  a  divisor  of  36  the  I.e.  m. 

3)1§ '4l §§  of  36,  54,  and  63  is  also  a  multiple  of 

o)b        9      ^1  i2.    12  may  therefore  be  rejected  from 

2        3         7  the  work. 

1.  c.  m.  =  22  x  33  X  7  =  756.  Divide  any  two  of  the  numbers  by 

a  common  prime  factor.  Then  divide  the  quotients  in  like  manner  until 
the  quotients  are  prime  to  each  other.  The  product  of  the  divisors  and 
the  last  quotients  is  the  1.  c.  m. 


Find  the  1.  c.  m.  of  : 

3.  24,  48,  72 

10. 

48,  64,  72 

4.  36,  70,  105 

li. 

144,  180,  240 

5.  32,  40,  48 

12. 

85,  51,  255 

6.  25,  35,  56 

13. 

120,  225,  540 

7.  30,  60,  105 

14. 

98,  42,  126 

8.  32,  48,  96 

15. 

180,  216,  120 

9.  45,  70,  90 

16. 

100,  110,  440 

CANCELLATION 

144  _:-  36  =  4.  We  may  separate  the  dividend  144  into 
the  factors  9  and  16,  and  the  divisor  36  into  the  factors  9 
and  4.     We  may,  therefore,  write  144  h-  36  =  4  as  follows  : 

(9x16)  -(9x4)  =  4. 

By  striking  out  the  common  factor  9  in  both  dividend 
and  divisor,  the  problem  is:    (16  -j-  4)  =  4. 

Striking  out  equal  factors  from  both  dividend  and  divisor 
does  not  change  the  quotient. 

When  the  product  of  a  number  of  factors  is  to  be  di- 
vided by  the  product  of  another  set  of  factors,  the  usual  way 
is  to  write  the  dividend  above  a  line  and  the  divisor  below, 
and  strike  out  equal  factors  : 


CANCELLATION  43 

Thus,  ^=2xl=Z=2i. 

Cancellation  is  the  process  of  shortening  operations  in 
division  by  striking  out  equal  factors  from  both  dividend  and 
divisor. 

Written  Work 

1.  Divide  3  x  6  x  8  x  20  by  11  x  4  x  20. 

2 

3x6x8x2p_36_os  Write  the  dividend  above  and  the  divi- 

11  X  4  X  20      ~  11  ~       !  T'     sor  helow  a  line.     First  cancel  the  20  from 

dividend  and  divisor.  Then  cancel  the 
factor  4  from  8  in  the  dividend  and  from  4  in  the  divisor,  leaving  2  in  the 
dividend  and  1  in  the  divisor.  As  there  are  no  other  factors  common  to 
dividend  and  divisor,  you  have  3x6x2,  or  36,  divided  by  11,  or  ff, 
which  equals  3T3T. 

Note.  —  When  equal  factors  in  the  terms  are  canceled,  the  factor  1 
always  remains,  but  as  it  does  not  affect  the  product,  it  need  not  be 
written. 

Divide  : 

2.  27  x  56  x  38  x  50  by    19  x  35  x  40 

3.  5  x  51  x  36  x  63  by    17  x    9  x  54  x  10 

4.  25  x  72  x  64  x  28  by    40  x  96  x  21  x   4 

5.  69  x  oG  x  45  x  27  by    23  x  45  x  63  x    9 

6.  72  x  48  x  84  x  28  by    24  x  48  x  42  x  14 

7.  148  x  64  x  57  x  12  by  114  x  32  x  48 

8.  By  selling  butter  at  24  ^  per  pound  a  lady  receives 
enough  money  to  buy  48  pounds  of  coffee  at  20^  per  pound. 
How  many  pounds  of  butter  does  she  sell  ? 

9.  A  man  worked  16  days  of  10  hours  each  at  20^  per 
hour,  and  spent  the  money  he  received  for  corn  at  40 ^  per 
bushel.     How  many  bushels  of  corn  did  he  get  ? 


FRACTIONS 

FRACTIONAL  UNITS 

When  we  say  8,  6  ft.,  $2,  6  rd.,  7  mi.,  5  in.,  what  are  the 
units  of  measure  ? 

Observe  that  in  each  case  the  number  and  its  unit  of 
measure  are  of  the  same  denomination ;  thus,  1  ft.  is  the 
unit  of  measure  in  6  ft. 

A  unit,  therefore,  is  any  single  quantity  with  which 
another  quantity  of  the  same  kind  is  measured  or  com- 
pared ;  as,  1  is  the  unit  of  10 ;  1  ft.  is  the  unit  of  8  ft.  ;  1 
yd.  of  2  yd.  ;  1  mi.  of  12  mi.  ;  1  acre  of  5  acres,  etc. 

A  fractional  unit  is  one  of  the  equal  parts  into  which  an 
integral  unit  has  been  divided  ;  as,  J^,  -|,  ^,  ^,  y1^,  etc. 

A  fraction  is  one  or  more  fractional  units ;  as,  |,  f ,  |,  |, 
•|,  etc. 

The  terms  of  a  fraction  are  the  numerator  and  the  denomi- 
nator. 

The  denominator  indicates  the  size  of  the  fractional  unit ; 
it  is  written  below  the  line,  and  shows  into  how  many  parts 
the  integral  unit  has  been  divided.  Thus,  in  the  fraction  |, 
5  is  the  denominator,  and  shows  that  some  unit  has  been 
divided  into  5  parts. 

The  numerator  indicates  the  number  of  fractional  units; 

it  is  written  above  the  line,  and  shows  how  many  parts  are 

taken.    Thus,  in   the  fraction   |,  4  is  the  numerator,  and 

shows  that  4  parts  have  been  taken. 

44 


FRACTIONAL   UNITS  45 

1.  What  is  the  fractional  unit  in  jj  ?  {  ?  |  ?  f  ? 

2.  Read  the  following  fractional  units  in  order  of  their 
size,  beginning  with  the  largest:    -,1,.,  |,  J,  y1^,  £,  |,  and  .,'j. 

3.  The  use  of  the  numerator  and  the  denominator  in 
T92  yd.  may  be  explained  thus,  -^  yd.  =  9  x  ^2-  yd. 

As  the  integral  unit  is  the  basis  by  which  we  measure 
whole  numbers,  so  the  fractional  unit  is  the  basis  by  which 
we  measure  fractions  of  the  same  kind. 

4.  Name  the  unit  of  4  ft.;  5  mi.;  f;  §. 

5.  Which  is  the  larger,  |  or  1  ?  |  or  1  ?  |  or  1? 
Explain  how  much  larger  in  each  case. 

6.  What  is  the  difference  in  value  between  the  fraction  | 
and  an  integral  unit  ? 

A  common  fraction  is  a  fraction  that  has  both  terms  ex- 
pressed; as,  f,  f,  \. 

A  proper  fraction  is  a  fraction  less  in  value  than  1 ;  as,  ^, 

7     3     4     1     1      3     pfp 
JT   4'    5'    91  T1  3'  euo" 

An  improper  fraction  is  a  fraction  equal  to  or  greater  in 
value  than  1 ;  as,  |,  f,  |,  f ,  f ,  ^g0-,  etc. 

A  mixed  number  is  a  number  expressed  by  a  whole  number 
and  a  fraction  ;  as,  3^,  12|. 

Change  each  of  the  following  to  integral  units,  or  to 
mixed  numbers.     Thus,  |  =  1^. 

10.  ^ 

11.  V 

12.  17- 


7. 

10. 

8. 

f 

9. 

6 

13. 

¥ 

16. 

¥ 

14. 

9 

17. 

¥ 

15. 

¥ 

18. 

¥ 

46 


FRACTIONS 


READING   AND    WRITING  FRACTIONS 


Read 
l. 

2. 
3. 
4. 
5. 


! 

6. 

15 
40 

8 
9 

7. 

4 
10 

1  1 
12 

8. 

45 
ft 

1 
6 

9. 

38. 
110 

H 

10. 

1  1  5 
21? 

11. 

12. 
13. 
14. 
15. 


s$12§ 
To  bu- 

6|  bbl. 

1  Qfi  6 


1  oz.  =  74iii  °f  a  ton. 


Write  in  figures  : 

One  fourth. 
Three  fifths. 
Six  ninths. 
Three  fourths. 
Seven  tenths. 


1. 
2. 
3. 
4. 
5. 

11. 

12. 

13. 

14. 

15. 

16. 

17. 

18. 


6.  Eighteen  twentieths. 

7.  Eight  thousandths. 

8.  Sixty  seventieths. 

9.  Nineteen  forty-thirds. 
10.  Eighty-nine  thousandths. 


Eighty-nine  three  hundredths. 
Twelve  and  three  fourths. 
Six  and  three  fourths. 
Five  and  one  half. 
Five  ninths  of  three  fifths. 
One  thousand  ninety-fourths. 
Nine  hundred  three  thousandths. 
Ten  and  three  fourths. 
19.    Four  hundred  ninety  and  six  thousand  twenty-four 
ten-thousandths. 


Write  in  words : 


20. 
21. 
22. 
23. 


4 
5 

L 
9 

11 
1^ 

i 


24. 
25. 
26. 
27. 


A 

35 
¥6 

11 

85 

1  05 
ITS 


28. 
29. 
30. 
31. 


45-9- 

"22  2 

-UU1000 

-LVU12000 


KEDICTIOX   OF    FRACTIONS 


REDUCTION   OF   FRACTIONS 


Reduction  is  the  process  of  changing  the  form  of  a  number 
without  changing  its  value. 

1.  Divide  both  terms  of  the  fraction  |  by  2.  How  does 
|  compare  in  value  with  l  ? 

2.  Multiply  both  terms  of  the  fraction  |  by  2.  How- 
does  |  compare  in  value  with  | '!  How  may  we  obtain  |  or 
•^2  from  |  ? 

Multiplying  or  dividing  both  terms  of  a  fraction  by  the  same 
number  does  not  change  its  value. 

Changing  a  fraction  to  higher  terms. 

1.  Explain  why  a  fraction  is  expressed  in  smaller  fractional 
units  when  it  is  changed  to  higher  terms. 

2.  Explain  why  changing  a  fraction  to  higher  terms  does 
not  change  the  value  of  the  fraction. 

Change : 

3.  i  to  12ths  6.  ^to^ths  9.  lJto72d& 

4.  |  to  24ths  7.  |    to  56ths  10.  |    to  63ds 

5.  f  to  18ths  8.  f    to  81sts  n.  |  to  96ths 


12.     f     =^     =  A  16' 

13       -9_  —  _?_     =  J-  17 

J-«.       in  —  en      —  on  ■*■'• 


5  _  J_        -     f_ 

6  "~  36        "  Y2 

-  •>  9 


TO-  60     —  90  ■L/*8       "4'0       ~6¥ 


*  -io  K  ?  ? 


14.     A  =  A     =A  18- 


■  i 


IT  — I?     _  58"  *""'      12  —  96     —  7  2 


15.        n       =  st       =  TTfO  ^•" 


_6_  — 


9     —  8T     ~  10¥  "•      11  ~"  132  ""99 

Written  Work 

l.    Change  f  to  27ths. 

27  -i-  9  =  3  Since  multiplying  both  terms  of  a  frac- 

5      5x3      15  ti°n  by  the  same  number  does  not  change 

q=q       S  =  27  ^  vame'  multiply  both  terms  of  the  frac- 

tion by  the  quotient  of  27  -*■  9,  or  3. 


48 


FRACTIONS 


Change 


2. 
3. 
4. 
5. 
6. 
7. 
8. 


|  to  20ths 
I  to  56ths 
l|  to  96ths 


T93  to  78ths 


11  to  276ths 


9. 

10. 

11. 

12. 

if  to  132ds  13. 

l|  to  72ds  14. 

-^  to  135ths  15. 

Changing  a  fraction  to  lower  terms  or  to  lowest  terms. 
1.    Explain  why  a  fraction  is  expressed  in  larger  fractional 
units  when  it  is  changed  to  lower  terms.     Explain  also  why 
changing  a  fraction  to  lower  terms  does  not  change  its  value. 

Change  : 

ff  to  12ths 


l|  to  275ths 
if  to  372ds 
f!  to  494ths 
!!  to  765ths 
fi  to  415ths 
|f  to  315ths 


2.  A  to  4ths 


6. 
7. 


12 

||  to  Cths 
|f  to  8ths 
|f  to  lOths 
£f  to  12ths 
|§  to  8ths 


8. 

9. 
10. 
11. 
12. 
13. 


||  to  Gths 
ff  to  9ths 
ff  to  lGths 


4  0 

50 


?  _  4  9 
12  —  8¥ 


14. 
IS. 
16. 
17. 
18. 
19. 


_?_ 
21 

? 

9 

9 

8 

9 
t 
? 

9 


21 
63 

_4_8_ 
10  8 

13^ 
144 

24 
64 

35_ 
5  6 

40 
Y2 


Written  Work 

A  fraction  is  expressed  in  its  lowest  terms  when  the  nu- 
merator and  the  denominator  are  prime  to  each  other. 

l.    Change  ||  to  lowest  terms. 

Since  dividing  both  terms  of  a  fraction  by  the  same 
number  does  not  change  its  value,  we  may  reject  by 
cancellation  all  the  factors  common  to  both  terms,  leav- 
ing the  factors  7  and  9.     Hence,  ££  =  J. 

Or  we  may,  in  one  step,  divide  both  terms  of  the  frac- 
tion by  their  g.  c.  d.,  6. 


m_ 

n_ 

7 

u 

~%7l 

:9 

Or 

g.c.d 

6 

42 

■f-6 

7 

54 

*-6 

9 

REDUCTION   OF    FRACTIONS  49 

2.    Change  |§£  to  lowest  terms. 

357  +  3  =  119  +  7  =  17      0rffcd-21     35T  - 21      17 
483  +  3      161  +  7      23      ur'S-c-a--^     483  +  21  =  23 

Cancel  all  the  factors  common  to  both  numerator  and  denomi- 
nator. Or,  divide  both  numerator  and  denominator  by  their 
greatest  common  divisor. 

Change  to  lowest  terms  : 
3. 

4. 

5. 

6. 

7. 

8. 

9. 
10. 
11. 

Changing  a  mixed  number  to  an  improper  fraction,  or  an 
improper  fraction  to  a  mixed  number. 


18 
24 

12. 

1  2  1 
"13  2 

21. 

125 
325 

30. 

4£5 
53  0 

39. 

4  14 
999 

25 
55 

13. 

54 
12 

22. 

3&5 
605 

31. 

75  0 
S2  5 

40. 

1  2ii 
189 

42 
49 

14. 

18 

28 

23. 

480 
66  0 

32. 

615 

94  5 

41. 

4  3  5 
630 

72 

81 

15. 

42 

4  8 

24. 

18  2 
196 

33. 

4i2 
504 

42. 

in 

1  96 

21 
36 

16. 

3£ 
42 

25. 

264 
333 

34. 

67  2 

936 

43. 

2  1  6 
270 

.24 

28 

17. 

58 
T4 

26. 

315 
34  5 

35. 

256 
92  4 

44. 

546 

5  88 

^5 

18. 

128 
176 

27. 

200 
450 

36. 

551 
62  1 

45. 

396 

4  :;  2 

22 

Y2 

19. 

94 
144 

28. 

£28 
624 

37. 

294 
476 

46. 

561 

783 

84 
96 

20. 

81 
96 

29. 

288 
444 

38. 

322 

504 

47. 

837 
945 

Change  to  an  improper  fraction  at  sight : 


1. 

If 

4.  31 

7. 

u10 

2. 

n 

5.  5| 

8. 

3-2- 
°15 

3. 

01 

~3 

6.  2| 

9. 

8  to  12ths 

11AM. 

1  "Mil..  AJOIH. 

—  4 

10.  1 2  to  3ds 

11.  8  to  6ths 

12.  10  to  5ths 


50  FRACTIONS 


Written  Work 

l.    Change  lllf  to  an  improper  fraction. 

1  _  5.  In  1  there  are  § ;  in   111    there  are   111 

-i-ii  iii    x  JL  -  -  JL5.5.      times  |,  or  £§s,  which   added    to   f   equal 

£56  I  8  --  JL5  8  "       5         "-     Hence'  *11*  equals^. 

J,-  "T"   6   —      5~ 

In  small  numbers  the  work  may  be  done  mentally,  only 
the  result  being  written. 


Change  to  improper  fractions : 


2. 

12f 

8. 

™H 

14. 

268Jft 

20. 

391ft 

3. 

15^ 

9. 

9* 

15. 

324f§ 

21. 

18** 

4. 

22| 

10. 

103f| 

16. 

502* 

22. 

901^ 

5. 

80ft 

11. 

118|i 

17. 

109^ 

23. 

100^ 

6. 

48Ti 

12. 

1,,J66 

18. 

600JJ 

24. 

390|| 

7. 

56i| 

13. 

*dit'l0  5 

19. 

305f 

25. 

231H 

26.    Change  -1|4  to  a  mixed  number. 

In  1  there  are  ?,  and  in  if8  there  are  as 
12  8  _  128  -7-  7  =  181       many  times  1,  as  7  is  contained  times  in 
7  128,  or  18f.     Hence,  if*  is  equal  to  18$. 

Every  fraction  is  an  indicated  division. 
Change  to  integers  or  mixed  numbers  : 


27. 

31 
15 

33. 

w 

39. 

34 

45. 

2  3^8. 
15 

28. 

_5_2JL 
11 

34. 

J70 
35 

40. 

876 

38 

46. 

14  4  0 
75 

29. 

955. 

7 

35. 

18 

41. 

24 

47. 

5286 

48 

30. 

13JL 
16 

36. 

625 
"2  5 

42. 

862 
"84 

48. 

4646. 
50 

31. 

261 

8 

37. 

,5  7  6 

24 

43. 

534 
96' 

49. 

2200 
12 

32. 

w 

38. 

.240 
16" 

44. 

121A 
24 

50. 

4  03  2 
"36 

REDUCTION    OF    FRACTIONS  51 

Changing  to  least  similar  fractions. 

A  common  denominator  of  two  or  more  fractions  is  a  num- 
ber that  contains  all  the  denominators  of  the  fractions  an 
integral  number  of  times  ;  thus,  24  is  a  common  denominator 
of  ^,  ^,  and  J. 

The  least  common  denominator  (Led)  of  two  or  more 
fractions  is  the  least  number  that  contains  all  the  denomina- 
tors of  the  fractions  an  integral  number  of  times  ;  thus,  12  is 
the  Led.  of  },  ^,  and  J. 

The  1.  c.  d  is  the  least  common  multiple  of  the  denominators. 

Similar  fractions  are  fractions  that  express  the  same  unit 
value.      They  must  therefore  have  a  common  denominator. 

By  inspection  : 

1.  Change  |,  |,  and  ^  to  similar  fractions  having  the  least 
common  denominator. 

It  is  evident  by  inspection  that  18  is  the  least  common 
multiple  of  2,  3,  and  9.  It  is  therefore  the  least  common 
denominator  of  the  given  fractions.  Changing  the  given 
fraction  to  ISths.  we  find  that  \  =  T\ ;  t=\t\  and 
s  =  jo.  Hence,  the  fractions  h  §,  and  |  may  be  changed 
to  the  similar  fractions  ^,  ff,  and  i§. 


Change  to  least  similar  fractions 
2. 
3. 
4. 
5. 
6. 


1  x  0_ 

2x9 

9 

:18 

2x6. 
3x6 

12 

=  18 

5  x  2  _ 
9  x  2~ 

1° 
18 

t 

3' 

1       5 

4'   12 

7. 

1 

5' 

3        7_ 
10'   40 

12. 

2 
3" 

1      19 
6"   36 

17. 

1 
6' 

3    JL 

7-14 

2 

3' 

1       2_ 

5'   15 

8. 

1 
3' 

A»A 

13. 

1 
3" 

1      1 
2*   6 

18. 

1 
3' 

1  •  •   2 

h 

3'   1? 

9. 

2 

5' 

3-     9_ 
"8"'  ¥5 

14. 

3 

7- 

1  1 
14'    -  - 

19. 

2 

5' 

2      3_ 

;;•    -JO 

i 

6' 

3     17 

-  •  21 

10. 

1 
9' 

1       -5_ 
6'    18 

15. 

3 

5       7 

If      1    ', 

20. 

4 

7" 

5       1 
8"'   5  6 

1 

9' 

_4_    _§_ 
18'   3  6 

11. 

3 

5' 

7      JL 

10'  2  0 

16. 

1 

1 

i  r  53 

21. 

■ 

l       3 

52  FRACTIONS 

By  factoring  the  denominators : 

l.    Change  |,  f ,  and  ^  to  similar  fractions  having  the  least 
common  denominator. 

4=2x2 

In  finding  the  I.e.  m.,  use  each  factor 

O  =  -i  X  o  as  0fteu  as  it  occurs  in  any  one  number. 

10  =  2  x  5 
1.  c.  m.  =  2x2x3x5  =  60 

3  x  15  =  45 

4  X  15       60  ,The  least  common  multiple  of  the  denominators  is 

5  x   10       50  ^'  w°icn  *s  the  least  common  denominator   of  the 
£  1  ft  ==  ~fU\  giyen  fractions.      Changing   the   given    fractions  to 

o  X     a     n  i     60ths'  we  find  that  I  =  M;  I  =»5  and  &  =  M- 
9  x     6_54 

10  x     6~60 

Change  to  least  similar  fractions : 

2  4     2     3     1  o       2     19     _5_    U  11      _L      L    J      29 
*'     4'   5'   8'  2                     °'      5'   20'   12'   30  x*'      10'   12'  20'   3~0 

3  2    _5_    _7_    1  o       1     1    _9      11  is        3      _9_    Q3     9H 
°*      3'   16'   12'  4              *'      7'  2'  28'    18                    xa"      1?'   16'  °8'  ^2  1 

4_7_i    _8_      9.        in       1    _9_    _8_    _3_  ic      J_    11      3        5  1 

*'      10'   5'   15'  20         1Ul      4'  10'  35'   16  -LO-     2  1'   35'  Y0'   120 

5  2     4     15  -n       _7_    J>_    11    li  17       5     8    _&_     31 
a*     IT'   5'   8'   6                  xx*      18'   15'  J9'  30  -L/<      6'   9'  2  1'  63 

6  &    12    11  io        1       _5_    _9_     31  in       8     14     Q  7 
°-      9'  2  5'   18f                 ""'     18'  2  1'  2  8'   54               xo-      9'  2  5'  °T5 

7  2     5     _8_  13      31     11     IS     12  iq         9      16     19       GJ 
'•     7'   9'   11                    ■LO-     °2'   18'  A6'  24               x*'     22'  3^'  66'   132 

ADDITION  AND  SUBTRACTION 

Size  and  kind  of  fractional  units. 

1.  Why  is  it  not  possible  to  add  4  ft.  to  5  oz.  ? 

2.  What  is  the  sum  of  \  and  |  ?  of  |  and  §  ? 

3.  What  is  the  size  of  the  fractional  unit  of  £  and  |  ? 

4.  What  is  the  kind  of  fractional  unit  in  each  ? 

5.  Are  the  fractional  units  of  |  and  |  alike  in  size  and 
kind  ? 


ADDITION    AND   SUBTRACTION  53 

6.  What  is  the  size  of  the  fractional  unit  in  $|  and  |  ft.? 
What  is  the  kind  of  unit  in  each  ? 

7.  Why  can  we  add  or  subtract  $  £  and  $-§,  or  £  ft.  and 

2    ff    9 

8.  What  kind  of  fractions  can  be  added  or  subtracted  ? 
Before  fractions  can  be  added  or  subtracted  they  must  be  ex- 
pressed in  similar  fractional  units. 

Fractions  having  the  same  kind  of  units  or  having  related  units  can 
be  added;  thus,  f  and  J,  or  f  yd.  and  \  ft.  (=  T\  yd.)  can  be  changed  to 
similar  fractions  and  then  added.  But  fractions  whose  units  are  unrelated, 
as  f  yd.  and  \  oz.,  cannot  be  added,  because  they  cannot  be  changed  to 
similar  fractions. 

9.  5.]   ft.  and  2  yd.  = ft.     Why  must  you  change 

yards  to  feet  before  adding  ? 

10.    Add  the  fractions  in  the  following  list  that  are  similar: 


\  da. 

|rd. 

3 
8 
2 
3 

hr. 
ft. 

3  fin                    -9- 

tV  min-       i 

min. 
ft. 

S  in-- 

ird. 

Add  quickly : 

11     1  +  1 

■"■■      2^4 

15. 

£_i_  1 
5^2 

19.     £  +  | 

23. 

5  4-1 

6  '    3 

12      2.4-1 
±di-      3    '    6 

16. 

4.1 
3^2 

20.        f+1 

24. 

1  4-  8 
3    •    6 

13       3  _i_  1 

17. 

2    .    1 
3^9 

21          -Ui 
**■■         5^2 

25. 

Bj.5 
4  +  ff 

14      1  4_  2 
J-*.      4  -t"  3 

18. 

5  _i_  3 

1+2 

22      I  1  4-  2 
12    '    3 

26. 

i+^ 

Written  Work 

l.    Find  the  sum  of  f,  |,  and  |. 

The  least  common  denominator  is  36.     Chang- 
ob  =  1.  c.  d.  jng  tjie  gjven  fractions  to  36ths,  we  find  that 

|  =  || ;  3  =  |i ;  |=  3|,    The  sum  of  these  fractions 


2 
3 

24 

! 

27 

8 
9 

32 

—  83  —  011 
-T5 36" 


8S  —   Oil 


1.  What  is  the  first  step  in  the  work? 

2.  "What  is  the  second  step  ? 


3  6  3  6  3.    What  is  the  third  step? 


54 


Add: 

o       5.     7    A  7       3     2    _9_  _9       3 

2.     g>   $,  f  /•     ■$,  ^    10  •"•     ^'   12'     32'  4 


FRACTIONS 

3 

4' 

2 

"5"' 

9 
10 

9 

T' 

9 
14 

3 
1   4 

2 

5' 

3 

7' 

1 
9 

2 
3' 

3 

5' 

1     5 

4'   6 

1 
'      6' 

2 
3' 

J7_    14 
12'    15 

o  3       9       1  o  2       9       3  13  1    _5_    _3_     11 

3.  y,  -J4,  2  **•  Y'   14'   4  A  8'   12'  16'  2  4 

a.  5     11     3  a  2     3     1  14  JL     2     11     25 

4-  Y'  "2  5'  f  9  5'   7'   9  ■'■*•  14'   7'  3  5'  4  9 

c  2     1      1  in  2     3     1     5  K  1     1    J_    12 

5-  31  ?i  2  -10-  3'   5'   4'   6  4'   5'   10'  2  5 

c  5       7      5  -n  12       7      14  16  1    -3     1    -7_ 

6-  8'   12'  6  ■""  6'   3'   12'   15  ±0-  4'   8'   5'   12 

17.    Find  the  sum  of  3^,  2$,  and  7ft. 


-jqq_]   0  (J  Since  the  numbers  are  mixed  numbers,  the  integers 

and  fractions  are  added  separately,  and  their  sums 
are  united.  The  sum  of  \,  f,  and  T4o  is  f^,or  lT3gV 
The  sum  of  3,  2,  and  7  is  12.      The  sum   of   12  and 


8i 


45 
100 


72  i  Ts^  is  13/^. 


12  +  ftj  =  12  +  lftft  =  13^ 

Add  : 

18.  3f,  7f,  9ft  24.  20f,  12Jf,  5|f 

19.  18ft,  3y,  9ft  25.  14ft,  32^,  23ff 

20.  8f,  10ft  16ft  26.  2f,  7f,  lift,  14ft 

21.  7f ,  12ft,  24ft  27.  90ft,  60ft,  73ft 

22.  16|,  30f,45ft  28.  3-i,  4f,  6f,  8ft 

23.  50ft,  48ft,  16J|  29-  84T2'  36i  33f'  39f 

30.  A  bicycler  rode  8|  miles  the  first  hour,  7|  miles  the 
second  hour,  6ft  miles  the  third  hour,  and  8^  miles  the 
fourth  hour.  How  many  miles  did  he  ride  in  the  four 
hours  ? 

31.  Find  the  distance  around  a  field  80|  rods  long  and 
60|  rods  wide. 

32.  Find  the  sum  of  the  improper  fractions  f ,  ff ,  ft'  io- 

33.  What  number  is  that  from  which  if  32ft  is  taken,  the 
remainder  is  23y9ft  ? 


ADDITION    AND   SUBTRACTION 


55 


Subtracting  fractions. 

What  kind  of  whole  numbers  can  bo  added  ?  what  kind 
of  fractions  ? 

In  adding  like  fractions  we  find  the  sum  of  the  numer- 
ators ;  in  subtracting  like  fractions  we  iind  the  difference 
of  the  numerators. 


l.    From  |  take  T3g 
72  =  1.  c.  d. 


J 

63 

3 
18 

12 

5  1  _ 

1  7 

~7  2  - 

2  4 

Written  Work 


Since  fractions  must  be  made  similar 
before  they  can  be  subtracted,  f  and  -Ag  are 
changed  to  72ds.  The  difference  between 
$|  and  \\  is  f|,  or  \\. 


1. 
2, 

3. 


Observe  the  ihret  steps  in  subtraction  of  fractions: 

Change  the  fractions,  if  necessary,  to  like  fractions. 
Take  the  difference  of  their  numerators. 
Change  the  difference  to  its  simplest  form. 


Find  differences 
2. 


3. 
4. 
5. 


I  _  3 

9  4 

JL  _  11 

10  1^ 

J 5L 

12    18 


2  5 
27 


11 
12 


6. 
7. 
8. 
9. 


5  5 
96 

1  1 
—  24 

1  3 
15 

-H 

2:? 
2  4 

14 
15 

0  3 
108 

_  1  3 
36 

10. 

11. 

12. 
13. 


i_i  _  in 

12    13 


2  3 
36 


13 
2  5 


21  _  12 
63    3  5 


15 
5  6 


1  S 

12 


14.    A  boy  wishes  to  buy  a  pair  of  skates  costing  8^,  but 
he  has  only  6f.      What  part  of  a  dollar  is  lacking? 


15.    From  |  take  f. 


16.  What  fraction  added  to  |  will  give  ||  ? 

17.  From  -|  of  an  acre  of  land,  subtract  |  of  an  acre. 

18.  What  part  of  a  teacher's  salary  remained  after  he  had 
spent  1,  A^-.  and  1  of  it  ? 


7 


56  FRACTIONS 

19.  The  minuend  is  |f,  and  the  remainder  f.  What  is 
the  subtrahend? 

20.  If  a  boy  spends  I  of  his  money  one  day,  \  of  it  the 
next  day,  and  has  $1£  left,  how  much  money  had  he  at  first: 

Subtracting  mixed  numbers. 

Written  Work 

1.  From  1\  take  3$. 

7\  =  6  +  |  +  \  =  6|.   The  integers  and  fractions  are 

36  =1.  C.  d.    subtracted  separately.     The  least  common  denomi- 

74  =  6|       45  nator  is  36.     Changing  the  fractions  to  36ths  we  find 

35       20  that   f=  H,  and  $=${}.      tt  ~  **  =  H-      6-3  =  3, 

o^      — |J  which   added  to  f£  =  3f|.      Hence,  the  difference 

3B  between  7J  and  3f  =  3f£. 

7w  subtracting  mixed  numbers  subtract  the  integers  and  frac- 
tions separately. 

Find  differences  : 

2.  7f-3T\  8.   6311-24^  14.   60^-35^ 

3.  9f-2f  9.   71^-19*  15-   71f!-54yf 

4.  18H-8|  io.    78JJ-18H  16.    39if-18ii 

5.  30i-20if       11.  92||-29il  17-  82H-45M 

6.  45i-24f  12.    82f|-29f|  18.    29^-llfi 

7.  50^-llf         13.    95|f-47ii  19.    20fi-15fi 

20.  If  I  pay  a  grocery  bill  of  $221  a  water  bill  of  $3£,  and 
a  gas  bill  of  $5§,  how  much  shall  I  have  left  from  2  twenty- 
dollar  bills  ? 

21.  The  sum  of  three  numbers  is  150.  The  least  number 
is  151  and  it  is  63|  less  than  the  greatest.  Find  the  other 
number. 


ADDITION   AND  SUBTRACTION  57 

22.  What  fraction  added  to  the  sum  of  £,  f,  and  -^g  will 
make  f  ? 

23.  If  5  is  added  to  each  term  of  the  fraction  f,  is  the 
value  of  the  fraction  increased  or  diminished,  and  how 
much? 

24.  Two  boys  undertake  to  save  $50  apiece.  When  one 
of  them  lacks  $8$  of  having  $50,  both  together  have 
$  84|.     How  much  has  each  ? 

25.  A  traveling  man's  grips,  when  starting  out,  weighed  as 
follows:  12$  pounds  and  19|  pounds.  Find  the  weight  of 
both,  and  the  difference  in  their  weight. 

26.  James  lives  1 1  miles  east  of  the  schoolhouse,  and 
Harry  l^g  miles  west  of  the  schoolhouse.  Find  the  sum 
of  the  distances  walked  by  both  each  day  and  the  distance 
James  walks  farther  than  Harry. 

27.  Eight  women  do  different  parts  in  making  a  finished 
garment.  The  cost  of  the  different  parts  is  1}^,  2|^, 
41  £  3|£  41^,  4f|  £  l£  and  T7^.  Find  the  cost  of  making 
one  garment. 

28.  Four  automobiles  finish  a  race  in  the  following  time: 
8T45  hours,  8|  hours,  7|  hours,  and  9^0  hours.  Find  the  dif- 
ference between  the  time  of  the  winner  and  each  of  the  others. 

29.  The  average  cost  per  mile  of  a  fleet  of  freight  boats  on 
the  Great  Lakes  was  :  coal  13f  £  crew  12f  £  repairs  17f£ 
supplies  7^.  The  average  cost  per  mile  of  a  freight  train 
hauling  the  same  freight  was:  coal  74 §£  crew  37^,  repairs 
19-^6  supplies  4|^.     Find  the  saving  per  mile  by  water. 

30.  A  drayman  hauls  freight  by  the  ton  from  the  depot 
to  a  village.  Find  the  amount  hauled  in  8  loads  weighing 
respectively  :  1|  tons,  ^  tons,  If  tons,  2y\  tons,  2f  tons, 
If  tons,  21  tons,  1^  tons. 


58  FRACTIONS 

MULTIPLICATION  OF  FRACTIONS 
To  multiply  a  fraction  by  an  integer. 

1.  1  +  1  +  1  +  1  =  how  many  whole  units  ? 

2.  ^  +  ^4-^  +  1  =  how  many  fractional  units  ? 

3.  How  many,  then,  are  4x1?  4x|? 

4.  Does  it  make  any  difference  in  the  process  of  multi- 
plication in  problem  3  whether  the  multiplicand  is  a  whole 
number  or  a  fraction  ? 

5.  What  term  of  the  fraction  A  is  multiplied  by  4  ? 

6.  |  may  be  multiplied  by  4,  thus  :  4  x  ^  =  — - — ,  or  -  =  2| . 

o  o  o 

Give  products : 

7.  6  x  §         li.      5  x  f  15.      5  x  y\       19.    16  x  I 

8.  10  X  |  12.     12  X  f  16.     15  X  f  20.     14  X  f 

9.  9xf         13.      7x|  17.    12  x  I  21.    13  xf 
10.    12  x  I          14.      7  x  I          18.      8  x  I  22.    11  x  T\ 

23.  In  multiplying  the  above  fractions  by  a  whole  num- 
ber, did  we  increase  the  size  or  the  number  of  the  fractional 
units  ? 

24.  How,  then,  may  any  fraction  be  multiplied  by 
an  integer  without  increasing  the  size  of  its  fractional 
units  ? 

25.  2  x  |  of  a  square  =  how  many  eighths  of  the  square? 
How  many  fourths  of  the  same  square  ?  Draw  figures  to 
illustrate. 

26.  How  does  |  of  a  square  compare  in  size  with  |  of  the 
same  square  ?     Draw  figure  to  illustrate. 


MULTIPLICATION  59 

27.  3  x  |  of  a  square  =  how  many  ninths  of  the  square? 
how  many  thirds  of  the  same  square  ?  Draw  figures  to 
illustrate. 

28.  How  does  |  of  a  square  compare  with  §  of  the  same 
square  ? 

29.  How  much  larger  is  the  fractional  unit  in  fourths 
than  in  eighths  ?  in  thirds  than  in  ninths  ? 

30.  How  can  we  increase  the  size  of  the  fractional  unit 
in  |  without  decreasing  the  number  of  fractional  units? 
in  |  ? 

31.  How,  then,  may  any  fraction  be  multiplied  by  an  in- 
teger without  increasing  the  number  of  its  fractional  units  ? 

Then<3xl=db'°4 

In  what  two  ways,  then,  may  we  multiply  a  fraction  by 
an  integer  ? 

Multiplying  the  numerator  or  dividing  the  denominator 
of  a  fraction  by  a  number  multiplies  the  value  of  the  fraction 
by  that  number. 

Give  products : 


32. 

8  x  | 

40. 

15  xf 

48. 

25  x  A 

33. 

9x^ 

41. 

11  x  A 

49. 

15  x  A 

34. 

11  x  f 

42. 

9  x* 

50. 

18  x  fl 

35. 

6x?k 

43. 

16  x  & 

51. 

12  x  Hh 

36. 

10  x  ^ 

44. 

7vU 
1    A   u:i 

52. 

36  x  }| 

37. 

9xf0 

45. 

3  x& 

53. 

42  x  Jf 

38. 

12  xf 

46. 

4  x  |f 

54. 

39  x*f 

39. 

18  x& 

47. 

5.  x  -y- 

55. 

64  x  A 

60  FRACTIONS 


Written  Work 


Since   multiplying  the  numerator  of  a 

1.  Multiply  g^  by  5.    fraction   multiplies  the  fraction,  5  times 

A    v    JL.  —  15  —  1  _3_      _7_  _  3  5   _  1   a_ 
A    32  —  32  —     32      S2  —  32  —  *52- 

When  possible,  use  cancellation. 
Multiply  : 

2.  -28Tb77  11.   |Jby72  20.    fi  by  96 

3.  f  by  10  12.    ii  by  108  21.    fe  by  54 

4.  f£byl5  13.   T^by57  22.    j*  by  28 

5.  f  by  8  14.   II  by  144  23.    ^  by  105 

6.  J{by27  15.  ft  by  135  24.  ^  by  96 

7.  11  by  35  16.  ^  by  21  25.  {  °  by  121 

8.  11  by  28  17.  £  by  16  26.  if  by  48 

9.  ff  by  144  18.  Tfaby72  27.  &-by69 
10.  H  by  70  19.  TVe  by  24  28.  J|  by  126. 

Finding  fractional  parts  of  an  integer. 

8  x  I  means  that  f  is  to  be  taken  as  an  addend  as 
many  times  as  there  are  units  in  the  multiplier.      Thus, 

3_i_.a_i_3i.a_i3i3_i_jj_i_3 

4    '    4    '    l+l  +  l    '    4T4T4' 

|  of  8  means  that  8  is  to  be  divided  into  4  equal  parts 
and  3  of  these  parts  are  to  be  taken. 

What  is  the  first  step  in  rinding  the  fractional  parts  of  the  whole  num- 
ber? the  second  step? 

While  the  process  of  finding  fractional  parts  of  a  whole  number  is 
classed  as  multiplication,  the  multiplicand  at  no  time  is  taken  as  an  ad- 
dend, but  is  partitioned,  that  is,  divided  into  equal  parts,  and  a  certain 
number  of  these  parts  is  taken. 

The  sign  x  is  read  "  of  "  when  the  number  preceding  it  is 
a  simple  fraction  ;  as,  §  x  $6  is  read  "|  of  $6." 


MULTIPLICATION  61 

|  x  12  mo.  means,    therefore,    3  x  (J  of  12   mo.)  or  3  x 

3  mo.  =  9  mo. 

3 

Or,    -  x  12  mo.  = — t^-  mo.  =  9  mo. 
4  £ 

Find  : 

1.  j    of  #80  6.  ^ofGOhr.  11.  ].]xl24 

2.  |    x42  7.  {^  of  30  da.  12.  ^  x  175 

3.  |    x  63  8.  I    of  47  13.  |$  x  450 

4.  fg  x  48  9.  I     x  100  14.  fj  x  720 

5.  |    x  20  10.  |     x  95  15.  |f  x  108 

Written  Work 

1.  If  the  Welsh  mills  turned  out  in  a  certain  year  576000 
tons  of  tin  plate  and  the  American  mills  ||  as  much,  find 
the  output  of  the  American  mills  for  that  year. 

2.  A  certain  post  office  in  one  year  handled  53678996 
pieces  of  mail,  of  which  f  were  letters.  Find  the  number  of 
letters  handled  at  that  post  office. 

3.  The  records  of  a  blast  furnace  show  1179360  tons  of 
iron  made  during  the  year.  If  |  of  this  iron  is  sold  as  No.  1 
iron,  find  the  number  of  tons  of  No.  1  sold. 

Multiplying  a  whole  number  by  a  mixed  number. 

Written  Work 

l.    Find  the  cost  of  48|  gallons  of  molasses  @  $.88. 
$.88  qp.88 

48f=40  +  8  +  f  48| 

.66   =  |  of  .88  ^ 

7.04    =8x.88  704 

35.20    =40  x  .88  352 


#42.90    =48|  x.88  #42.90 


62  FRACTIONS 

Find  the  cost  of: 

2.  27§  tons  of  hay  at  #12  a  ton. 

3.  31|  yards  of  cloth  at  $  .24  a  yard. 

4.  10|  ounces  of  gold  at  #  18.75  an  ounce. 

5.  196T97  ounces  of  silver  at  $.46  an  ounce. 

6.  97|  bushels  of  apples  at  $.70  a  bushel. 

7.  68|  bushels  of  berries  at  #2.65  a  bushel. 

8.  147^  bushels  of  potatoes  at  $.85  a  bushel. 

9.  84^  pounds  of  prunes  at  $.12  a  pound. 

10.  257 1  feet  of  curbing  at  $.38  a  foot. 

11.  A  street-car  conductor  collects  on  an  average  $3.60 
per  hour.     How  much  does  he  collect  in  11|  hours? 

12.  In  4  days  a  carpenter  worked  7|  hours,  8  hours,  7^ 
hours,  and  6|  hours.  How  much  did  the  work  cost  at  45^ 
per  hour  ? 

13.  A  ditch  costs  $.27  a  rod.     Find  the  cost  of  227J  rods. 

14.  The  "Pennsylvania  Special"  averages  58  miles  per 
hour.      How  far  does  it  travel  in  16|  hours? 

15.  A  roller  in  a  steel  mill  rolls  118|  tons,  221^  tons,  193^ 
tons,  and  180|  tons  in  four  days.  If  he  is  paid  $.12  per  ton, 
how  much  should  his  pay  envelope  contain  for  the  four  days' 
work? 

16.  A  car  load  of  corn  contains  821|  bushels.  How  much 
is  it  worth  at  $.57  a  bushel? 

17.  Three  men  in  a  day  cut  respectively  2^  cords,  If 
cords,  and  2|  cords  of  wood.  How  much  does  each  receive 
for  his  work  at  $1.25  per  cord  ? 

18.  At  $26  per  ton,  how  much  will  the  rails  for  18  miles 
of  railroad  cost,  if  it  takes  158|  tons  per  mile  ? 


MULTIPLICATION 


63 


19.  Two  men  work  respectively  23]  days  .and  27|  days  in 
a  month.  How  much  more  does  one  earn  than  the  other,  it' 
each  receives  $2.25  per  day  ? 

Multiplying  a  mixed  number  by  an  integer. 
In  the  problem  9  x  3|,  which  number  is  the  multiplier? 
the   multiplicand  ?      The    multiplier    usually  precedes    the 


sign   X  • 

Give  products  : 

1.      9  x  9i- 

8. 

14x3$ 

15. 

11  x7f 

2.      6x| 

9. 

11  x5| 

16. 

25x4§ 

3.      8  x  5J 

10. 

6x8| 

17. 

13x31 

4.      7  x  8f 

11. 

18x3f 

18. 

12  x  15| 

5.      9  x  8£ 

12. 

20x4f 

19. 

15  x  7f 

6.    10  x  10T3o 

13. 

16x3| 

20. 

8x9| 

7.    15x31 

14. 

9xll-J 

21. 

9  x6ft     . 

Written  Work 

1.    Multiply  14§ 

by  9, 

143 

9 

9x 

t  =  ¥ 

=  3f. 

3|  =  9x| 

9x14  =  12U. 

3f  +  126  =  129f. 

126   =9x14 

.     129f  =  9  x  14 

.3 

8 

Multiply: 

2.    12f    by  28 

8. 

44|1  by  14 

14. 

47f    by  96 

3.    11$    by  45 

9. 

78|    by  63 

15. 

609f    by  21 

4.    14 A  by  CO 

10. 

89-^  by  105 

16. 

105|     by  49 

5.    25 11  by  75 

11. 

715f  by  45 

17. 

290T%  by  45 

6.    85f|  by  68 

12. 

101$  by  63 

18. 

21 3f    by  78 

7.    64 \l  by  56 

13. 

205f  by  75 

19. 

735|     by  21 

64 


FRACTIOXS 

Find  products: 

20.  213  x  609f 

25.  596  x  56f 

30. 

379  x  49T^ 

21.  612  x  48§ 

26.  972  x  32f 

31. 

49  x  465 1| 

22.  842  x  95| 

27.   96  x  325f 

32. 

786  x  49| 

23.  728  x  34T% 

28.  856  x  98| 

33. 

9872  x  36^- 

24.   96  x  207 § 

29.   54  x  657| 

34. 

4398  x  94| 

35.  There  are  16^  ft.  in  a  rod.  How  many  feet  are  there 
in  12  rods  ? 

36.  Find  the  cost  of  35  tons  of  railroad  iron  at  $38|  a 
ton. 

37.  At  i$lf  each,  how  much  will  40  "General  Histories" 
cost? 

38.  If  I  sell  7  apples  for  10  cents,  how  much  shall  I  re- 
ceive for  7  dozen  apples  ? 

39.  When  oranges  are  sold  at  3  for  10  cents,  how  much 
will  3  crates  carrying  180  each  cost  ? 

40.  Stephenson's  locomotive  weighed  4|  tons.  Find  the 
weight  of  a  modern  freight  mogul  weighing  40  times  as 
much. 

41.  A  mail  boy  averaged  13-|^  per  hour  for  117  hours 
worked  during  the  month.     Find  his  earnings  for  the  month. 

42.  A  residence  is  lighted  by  21  incandescent  lights. 
The  cost  of  each  light  per  day  is  1  f  ^.  Find  the  total 
electric  light  bill  for  a  year  of  365  days. 

43.  The  average  shipment  of  ore  from  a  mine  per  week  of 
6  days  is  347  tons.  If  $12^  is  the  average  profit  realized 
from  each  ton  of  ore,  find  the  net  profit  for  40  weeks. 

44.  A  mail  carrier's  deliveries  average  23 1  pounds.  How 
many  pounds  of  mail  does  he  deliver  in  2  trips  each  day  for 
312  days? 


MULTIPLICATION  65 

45.  Iii  a  certain  shoe  factory  a  pair  of  shoes  is  finished 
every  3|  minutes.  Find  the  number  of  days  of  10  hours 
each  required  to  make  4600  pairs. 

46.  An  establishment  consumed  in  one  year  8450  pounds 
of  twine  at  9^  per  pound  ;  36|  dozen  bottles  of  ink  at  $1.90 
per  dozen  ;  6  gross  pens  at  90  ^  per  gross ;  500  pads  of 
paper  at  f  $  per  pad.    Find  the  total  cost  of  the  purchase. 

47.  A  real  estate  agent  sold  6  pieces  of  land  containing 
respectively :  10§  A.,  121  A.,  18f  A.,  26j%  A.,  30§  A.,  3|  A., 
at  1250  per  acre.     Find  the  amount  of  the  sale. 

48.  A  town  has  a  population  of  3600.  If  the  average 
amount  of  water  used  by  each  person  is  6|  gallons  per  day, 
find  the  number  of  gallons  of  water  used  in  90  days. 

49.  If  a  motorman  receives  9\  per  hour,  how  much  does 
he  earn  in  7  weeks  of  6  days  each,  working  10  hours  per  day  ? 

Finding  fractional  parts  of  a  fraction. 

1.  What  is  i  of  9  hours  ?  §  of  9  feet  ? 

2.  What  is  i  of  9  tenths  ?  §  of  9  tenths? 

3.  1  of  9  tenths  means  that  we  are  to  take  l  of  9  parts  of 
a  unit  that  has  been  divided  into  10  equal  parts. 

4.  |  of  T97  =  how  many  tenths  ? 

5.  If  ^  of  t9q  =  ^,  how  much  is  §  of  T9a  ? 


Find  mentally : 

6.    loft 

11. 

7      of  £1 
9      OI  TS 

16. 

2 
3 

Of  -9- 
01   16 

7.    fof^ 

12. 

11  of  £± 

12  U1  33 

17. 

5 

0 

off 

8    4  of  14 
o.     8  ui  21 

13. 

_9_  of  4  0 
10  U1  ?3 

18. 

1  1 

12 

off 

9.    foflf 

14. 

_4.  Of  A5 
15  Ui   5  3 

19. 

:» 
1  D 

of| 

10.    *  Offl 

15. 

3      of  H 
8      Ui   3  5 

20. 

B 

8 

Of    ft 

HAM.    COMPL 

.     A  KITH. 

—  5 

66  FRACTIONS 

21.  What  does  the  expression  ^  mean  ? 

22.  Can  T97  be  separated  into  3  equal  parts ;  thus,  T^-,  T3^, 
^,  without  changing  the  size  of  the  fractional  unit  ? 

23.  To  what  fractional  unit  must  we  change  f  before  we 
can  separate  it  into  4  equal  parts  ;  that  is,  take  \  of  |  ? 

24.  Is  |§  the  same  in  value  as  f  ? 

25.  When  ||  is  separated  into  4  equal  parts,  how  many 
fractional  units  are  there  in  each  part  ? 

26.  Then  1  of  |  =  how  many  twentieths  ? 

27.  Observe  that  -  of  ?  =  L*!*  or  A. 

4       5     4x5'       20 

28.  What  18  f  Of  |?      Ifl0ff=,3_,30ff  =  3xJL    orJL 

29.  Observe  that  -  of  -  =  !L*J*,  or  — . 

4       5     4x5'       20 

A  fractional  part  of  a  fraction  equals  a  fraction  times  a 
fraction. 

Written  Work 

l.    Find  |  x  |f. 

7  X  16       7x  16  _    112  _  2  To  find  I  x  if  means  to  find  J  of  |f. 

8  x  21 "  8  x  21 ==  168 "~  3    *  of  H  =  A  and  J  of  h  =  7  x  A  =  W, 

or*. 


Or, 

2 

?  y=? 

$x&l    3 

3 

A  fractional  part  of  a  fraction  is  found  by  multiplying  the 
numerators  for  the  numerator  of  the  product  and  the  denomina- 
tors for  the  denominator  of  the  product. 

Indicate  the  operation,  and  cancel  when  possible. 

A  fractional  part  of  a  fraction  is  sometimes  called  a  com- 
pound fraction.     Thus,  \  of  \  is  a  compound  fraction. 


MULTIPLICATION  67 

An  integer  may  be  expressed  in  fractional  form,  thus,  — 

2 

8  =  8.        |of8  =  -3off  =  |  =  6. 

Find  products : 

r>        3     v   IB         a      2r'   v    14  lO      ?5  y    ij         14       %k     X  ^M 

o         5     v   38  7       21   v     33  in        21  y  15.5         15         :;  s     X    MS4I 

3*      19   X  3  5  7-      44   X     5  6  ■LJ"      6  2   X    162         XO'       43     A    130 

d.        15    v    14  o        IS   v     (!5  12        1  3    y     3  4  ic       54  3    x    102 

4-  2%    X  2  5  B-      2  6   X     7  2  X^'      68*39  xo*      5  12    A  2  4  5 

e        5  1     v     8  Q        1  1    v     4  6  i  -a        7  1    y    3  7  17        111   y  110 

5-  6  4    X  IT         9-     6  9  X  121  13-     74   X    38  L/'     220  x  4  1  1 

18.  Find  I  of  12|. 

Note.  — Change  the  mixed  number  to  an  improper  fraction. 

Find  : 

19.  §     of  7j  23.  3|     X  45  27.  2|    x  7 1 

20.  f     0fl2|  24.  7|     X|  28.  8|    x5| 

21.  I    ofl3f  25.  5T%x{|  29.  7|    x3| 
Tr  of  10$  26.  8|    x  I  30.  4T^  x  3§ 

Find  the  value  of : 

31.  4$  x  6f 

8  5      6 

A  Q      /-A       3$      48       30      ^^  QA 
4fx6f  =  |-xy  =  T,    or  30. 

32.  6|    x2T3Tx7|  38.    35^x22^x12 

33.  8^    x2|    x2|  39.  51fx  19^x121 

34.  101   x  11    x  7}  40.  6f  x  6|      x  I  x  2& 

35.  14j    x  17|  x  8|  41.  20)  x  20f     x  20{i  x  10 

36.  27*fx42fx6J  42.  7§.]xl5       x2|£xl2$ 

37.  2i  x  3|  x  4|  x  5|  43.  172.]  x  2./5     x  3£ 


22 


68  FRACTIONS 

44.  The  schedule  of  a  train  between  two  cities  is  12| 
hours,  and  the  train's  speed  is  35^  miles  per  hour.  Find 
the  distance  between  the  places. 

45.  Find  the  number  of  tons  of  sugar  cane  on  19 1  acres, 
if  the  average  number  of  tons  per  acre  is  11 §  tons. 

46.  An  automobile's  average  rate  of  speed  is  25  ^  miles 
per  hour.     How  far  does  it  travel  in  3|  hours? 

47.  Estimate  the  value  for  one  season  of  a  Vermont 
sugar  camp  at  <$  J^-  per  pound  if  6-|  pounds  are  obtained  on 
an  average  from  each  of  1275  maple  trees. 

DIVISION  OF  FRACTIONS 
Dividing  a  fraction  by  an  integer. 

1.  15  -5-  5  means  that  15  is  to  be  separated  into  5  equal 
parts  of  3  units  each ;  and  one  of  the  equal  parts  taken  ; 
thus,  15-^5  =  3.  Explain  in  the  same  way  what  18  -*-  9 
means. 

2.  \^  -5-  5  means  that  ^|  is  to  be  separated  into  5  equal 
parts  of  j2g  each,  and  one  of  the  equal  parts  taken  ;  thus,  || 
-i-  5  =  T2g.  Which  term  of  the  fraction  was  divided  by  the 
integer? 

A  fraction  may  be  divided  by  an  integer  by  dividing  the 
numerator  of  the  fraction  by  the  integer. 

Divide : 


3.     §  by  4 

5. 

15  j- 5 

2  6    *    ° 

•>■    IfbyS 

4.  if  by  6 

6. 

-3-S-^  9 
3T   •   v 

8.    |f  by  7 

9.    In  |  -s-  5,  can  you  separate  |   into  5  equal   parts   in 
which  the  fractional  unit  is  thirds? 


DIVISION  09 

10.  Can  you  divide  §  by  5  by  dividing  the  numerator  by 
the  integer  an  integral  number  of  times  ? 

11.  |  -i-5  means  that  |  of  |  is  to  be  taken.  Since  -\  of 
2  —  -2-   then    2-  —  5  =  -?- 

12.  |  =  yV  Can  {5  be  separated  into  5  equal  parts  of  T2^ 
each  ?  Then  §  -h  5  =  ^.  Observe  that  multiplying  the 
denominator  of  |  by  5  changes  the  fractional  unit  from 
thirds  to  fifteenths  and  takes  one  of  the  5  equal  parts  into 
which  §  has  been  changed. 

A  fraction  may  be  divided  by  an  integer  by  multiplying  the 
denominator  by  the  integer. 

Solve  the  following  problems  by  the  more  convenient 
method  and  give  your  reasons : 

13.  fft  +  7  16.      J^6  19.      T%-*-25 

14.  1-8  17.    T%%  -=-  9  20.    iff  +-  15 

is      25.  _s_  1  fl  la     _fi_  -s-  3  21        P  -*- 7 

Written  Work 

1.    Divide  ||  by  8. 

04       o    "  o  1°  a  the  division  is  performed  by  divid- 
er.  - —  =  —                 ing  the  numerator  by  8. 

25  25 

~  .  ^  .         „         In  b  the  division  is  performed  by  multi- 

b.    — — - — =—  =  —    plying  the  denominator  by  8,  and  changing 
ZQ  X  o      200      ^5    tne  fraction  to  its  lowest  terms. 

Q 

In  c  the  division  is  indicated  and  the  quo- 


c. 


3 

=  —  tient  is  found  by  cancellation. 

25  x  8     25 


A  fraction  may  be  divided  by  an  integer  either  by  divid- 
ing the  numerator  or  by  multiplying  the  denominator  of  the 
fraction  by  the  integer. 


70 


FRACTIONS 


Find  quotients: 


2.  |  +  5  11. 

3.  |  -5-  9  12. 

4.  ft  +  7  13. 

5.  f^l8  14. 

6.  11  -=-  5  15. 

7.  T82°o-25  16. 

8.  1|  -4-  7  17. 

9.  II  -5-  8  18. 
10.  T9Y  -=-  5  19. 
29.  Divide  3|  by  5. 


21^« 
65    ■    ° 

31    •    y 

_8_  ^_  24 

2  1    ' 


12 
13 


16 


19    •    "' 

16  ^40 

36  ^_  19 

37  *    Xii 


12 


ii 

18 


3  5  ^.42 

4  3     *    *^ 


31  =  25 

°8  8  ' 


25     . 

8 


5 

25 

8xp 


5 

8 


20. 

21 
28 

-18 

21. 

12 

83 

-30 

22. 

96 
113 

-64 

23. 

51 
61 

-38 

24. 

132 
16  3 

-48 

25. 

111 
12  7 

-52 

26. 

11  1 
112 

-37 

27. 

256 
"2  7  5 

-80 

28. 

180 
19T 

-HOO 

Note.  —  Small  mixed  numbers  are  frequently  reduced  to  improper 
fractions  and  then  divided  by  the  same  principle  as  proper  fractions. 


30. 
31. 
32. 
33. 
34. 
35. 


2f-6 
41-1-7 

4T«T  h,  13 


922 

^2  5 
51  3 


48 
23 


17J  +  8 


36. 
37. 
38. 
39. 
40. 
41. 


28f  -  25 
284  h- 18 


32-8- 


21|  -4-  25 

181  +  26 

19JTV45 


21 


48.  Divide  1286f  by  9. 


42. 
43. 
44. 
45. 
46. 
47. 


10T23  +  24 
29f  +  "12 


22ft 
30| 

191 


58 
23 
26 


211  _=_  56 


9)1286f 


142f| 


Note.  —  The  division  may  be  performed  by  changing  both  numbers 
to  sevenths,  but  it  is  a  much  shorter  process  to  perform  the  work  as 
indicated,  changing  the  remaining  mixed  number,  8f,  to  an  improper  frac- 
tion, V,  and  dividing  it  by  9.     Thus,  \  of  -6?2-  =  If- 


DIVISION 

49. 

25681^  -s-7 

54. 

8002 fa 

-12 

50. 

9863^  -=-  6 

55. 

1428*1 

-5-12 

51. 

6532^h-8 

56. 

10935| 

-4 

52. 

6879^  -5-  5 

57. 

9720| 

-5-11 

53. 

36370|^-11 

58. 

7090^ 

-5-9 

71 


Dividing  fractions  by  first  making  them  similar. 

1.  What  is  the  unit  of  measure  in  eaeh  of  the  following : 
8  ;   6  yd. ;   5  ft.  ;   4  in. ;   8  rd. ;   5  oz.  ;   2  lb. ;   10  mi.? 

2.  What  kind  of  units  may  be  added  or  subtracted  ? 

3.  Since  both  the  dividend  and  the  divisor  of  concrete 
numbers  must  represent  like  units,  to  divide  24  yd.  by  3  ft. 
we  must  either  change  yards  to  feet,  thus,  72  ft.  -5-  3  ft.  ;  or 
feet  to  yards,  thus,  24  yd.  -=-  1  yd. 

4.  In  |  -5- 1  are  the  fractional  units  alike  in  size  and 
kind?     Then  how  often  is  |  contained  in  |? 

5.  Since  |  is  contained  3  times  in  |,  how  can  we  divide 
one  fraction  by  another  when  the  denominators  are  alike? 

A  fraction  may  be  divided  by  another  fraction  by  chang- 
ing both  fractions  to  a  common  denominator  and  dividing  the 
numerators. 

6.  Divide  f  by  f . 

3  _  JL .      5  _  1 0 

¥  —  12'      6  —  12 
JL  _=_  1  0  _  Q  _:_  1  ()  —  JL 
12    *    12  —  V    '    ±XJ  —  i7 

Find  quotients  : 


8.     X  -=-1  12. 


o 
9 

.     n 
•    6 

T52- 

!_   2 

•    3 

9 

_  3 
5 

1  3 

15 

3 

JL 
11 


16-  tf  +  J 

17  5.       _;_   1 

-1,3-      16    •      3                          ■L/#  1?    '    9 

10.    U  +  f                  !*•♦  +  ♦                  18-  H  +  l 


72 


FRACTIONS 


By  inverting  the  terms  of  the  divisor  and  multiplying. 

1.  How  many  half  inches  are  there  in  1  in.?  in  2  in.? 
3  in.  ?  4  in.  Then  how  many  times  is  ^  contained  in  1?  in 
2?  in  3?  in  4? 

2.  If  1  -j-'J  =  4,  what  does  2  +  \  equal  ?  3  -  \  ?  12  +  \  ? 


3.    What  does  1  -f-  l  equal  ?  3  -=-  l  ?  6  -=- 


i  ? 


To  divide  any  number  by  a  fractional  unit  multiply  the  num- 
ber by  the  denominator  ;  thus,  12  h-  \  =  12  x  ^  =  ^  or  48. 


4. 

5. 

6. 
13. 
14. 
15. 
16. 


12  —  1 


15 

16 


? 


1   _  9 
3  —  • 


7. 
8. 
9. 


10  -^  -1  =  ? 


io.    20-^i  =  ? 


11. 


25h-£  =  ? 


9-  iW 

9-hTV  =  ?  12.    18-^1  = 


1  -s- 1  =  how  many  ? 
1  -=-  |  =  how  many  ? 
1  -s-  -Jj  =  how  many  ? 
1  -=-  |    =  how  many  ? 


17.  1  -=-  j5q  =  how  many  ? 

18.  1  -f  Jj  =  how  many  ? 
1  -=-  §  =  how  many  ? 
1  -=-  |    =  how  many  ? 


19. 
20. 


Observe  that  the  number  of  times  each  of  the  above  frac- 
tions is  contained  in  1  equals  the  number  of  times  the 
numerator  is  contained  in  the  denominator. 

The  number  of  times  a  fraction  is  contained  in  1  is  called 
the  reciprocal  of  the  fraction.  Thus,  f  is  contained  in  1,  | 
times.     Hence,  |  is  the  reciprocal  of  §. 

1  divided  by  any  fraction  equals  the  fraction  inverted. 

Find  quotients  : 


21. 

8^|             23.       4  +  | 

25.     10-5-1 

27.    25 

22. 

6H-|             24.    15-^-f 

26.    12  -f 

28.    14 

29. 

|  -=-  |  =  how  many  ? 

2  _t 

3  • 

3  —  2    v    4  _  8               Since  1 
"  4  —   3    X    3   —  9                °U 

.      3    _    4        2  ^   3   _ 
•     ?  —    3>     3     •     ¥  ~ 

|  of  |,  or  |. 

DIVISION 


7:; 


Any  number  is  divided  by  a  fraction  by  inverting  the  terms 
of  the  divisor  arid  multiplying. 

30.    Work  if  -r-  |  by  both  methods.     What  principle  does 
the  second  method  introduce  that  the  first  does  not? 

Note.  —  The  process  should  be  shortened  by  cancellation  when  possible. 

Written  Work 


Change  the  mixed  numbers  to 


improper  fractions  before 


dividing.      Divide : 

1. 

18  by  f 

20. 

13     _ 

18 

.    26 
■    2  7 

39. 

119.        7 
T3  8    •     US' 

2. 

12  by  | 

21. 

5 

2  2 

3 
5 

40. 

85       .51 
87"       '    1J5 

3. 

25  by| 

22. 

2  7      _ 
32 

l.     9 

'    16 

41. 

3  9       .13 

6  4       *24 

4. 

32  by  if 

23. 

2  5      _ 

3  6 

.    15 
16 

42. 

993    .    95 

^"4    *    -8 

5. 

40  by  f  § 

24. 

28 
39 

_  42 
65 

43. 

45|  -4-  5« 

6. 

48  by  1| 

25. 

65      _ 
7  2 

5 

8 

44. 

6*  +  8| 

7. 

172- 

8 
9 

26. 

13  3  _ 

1  4  4 

95 
192 

45. 

128  ■*-  17/2 

8. 

235- 

4 
5 

27. 

99    _ 
12  5 

209 
2  r.  0 

46. 

160  by  f  of  | 

9. 

770- 

-  11 
15 

28. 

81    _ 
1  12 

45 
"72 

47. 

|  of  640  by  6£ 

10. 

882- 

_  3 

Y 

29. 

_4_9_  _ 

1  II  s 

91 
132 

48. 

198  by  12f 

11. 

1035- 

_   5 
6 

30. 

243 

2  56 

189 
32  0 

49. 

8|  +  4J 

12. 

984- 

_   3 

31. 

1  96  _ 
22  5 

_    56 
3T5 

50. 

10|  -*-  6f 

13. 

3      _ 
I 

2 
3 

32. 

185  _ 

22  4: 

111 

896 

51. 

101^31 

14. 

2 
3 

_  3 
1 

33. 

175  _ 

282 

125 
"375 

52. 

(f  Of  f)  -4-  (J  Of  |) 

15. 

1 

8 

_   3 
4 

34. 

23  0  _ 
231 

2 
33 

53. 

(f  of  £) -*-(f  of  f) 

16. 

9    _ 
10 

_   3 

5 

35. 

143  _ 
lYO 

l.    6  5__ 
'    136 

54. 

(4  (>f  «)  +  (A  0 

17. 

13  _ 
1? 

6 
Y 

36. 

114 

-A 

«  "f  H) 

18. 

7    _ 
12 

2 
3 

37. 

8  3 

S4 

_    5 
5  6 

55. 

(H^W+H 

19. 

15  _ 
16 

_    1  1 
24 

38. 

55     _ 

7  9       " 

22 

56. 

(«ofH)+(jofft: 

74  FRACTIONS 

Miscellaneous 

1.  At  $1|-  per  day  how  long  will  it  take  a  laborer  to 
earn  $671? 

2.  Divide  |  of  |  of  J  by  f  of  *  of  Jf 

3.  A  man  who  owned  T7y  of  an  estate  sold  |  of  his  share. 
What  part  of  the  estate  did  he  then  own  ? 

4.  A  man  who  owned  f  of  a  store  sold  |  of  his  share  for 
$1406.25.  What  was  the  value  of  the  store?  What  part 
had  he  left  ? 

5.  One  man  has  $35|  ;  another  has  $62|.  If  each  gives 
to  the  other  §  of  what  he  has,  how  much  more  will  the  one 
then  have  than  the  other  ? 

6.  If  |  of  10  bushels  of  oats  cost  |3f,  how  much  will  20| 
bushels  cost  ? 

7.  What  number  must  be  multiplied  by  £  of  3|  to  give 
a  product  of  32 -^  ? 

8.  A  storm  moves  eastward  at  the  rate  of  18^  miles  per 
hour.  In  how  many  hours  after  the  storm  is  first  observed 
in  Chicago  should  it  be  due  in  Pittsburg,  468  miles  east  ? 

9.  Kerosene  oil  weighs  6|  pounds  to  the  gallon.  Find 
the  number  of  gallons  in  a  tank  car  of  oil  weighing  39200 
pounds. 

10.  A  steam  threshing  machine  averages  If  bushels  of 
wheat  per  minute.  How  many  minutes  at  the  same  rate 
will  it  take  to  thresh  358|  bushels? 

11.  The  average  cost  of  the  education  per  pupil  in  a 
certain  city  is  $51.  If  the  total  cost  is  $16480,  find  the 
number  of  pupils  attending  school. 

12.  A  contractor  employs  6  men  for  27|  days  and  pays 
them  $363.     Find  the  average  daily  wages. 


COMPLEX   FRACTIONS  75 


COMPLEX  FRACTIONS 

A  complex  fraction  is  a  fraction  which  has  a  fraction  or  a 
mixed  number  in  either  or  both  of  its  terms. 

Thus,     -2 ,     — ,     £,     !i2     are  complex  fractions. 
'      o'      3'      4'     41  r 

0        8         5        ^? 

Such  examples  are  simplified  by  the  principles  of  division 
of  fractions. 

Thus,     £  =  -  ■*■  3  =  -.     They  rarely  occur   except  in  ad- 

o         —  O 

vanced  courses  of  study. 

Written  Work 

l.    Find  the  quotient  of  2J  divided  by  § . 

3 

6  2 

Simplify  : 
1  4  of  21  ,„     |x6| 

o        9  7       5  5  12.     A_ a 


9  7.     5  *"  -5  12. 

?i  if 


3 
_8. 


°3     •    8 


11  ,    ,  44 

3.    1|  8.    |X|  13.     |0f-£ 

4      W  9.    _LJ  14.     A  Of! 

5  S  +  2i  10    Six  I'  8-gbtt) 

6  (-fe-Dx(t  +  |)     u    (i°f8j)-j  16    (21x31)-,- If 


76  FRACTIONS 

FRACTIONAL   RELATIONS 
Finding  what  part  one  number  is  of  another. 

1.  What  part  of  12  is  4?  What  part  of  18  is  5?  Ex- 
press the  answers  also  in  the  form  of  division.  Thus, 
T42=4-12;  t\=5h-18. 

2.  What  part  of  |  is  f  ?  of  |  is  f  ?  How,  then,  can  we 
find  what  part  one  number  is  of  another? 

Divide  the  smaller  number  by  the  larger  number. 

Written  Work 

1.  What  part  of  208  is  96? 

cm   •   908        96   -5-  16  _     6  We  divide  the  smaller  number  96 

"  208  —  16  "  13      ky  208,  and  reduce  the  resulting  frac- 
tion 29jfg  to  its  lowest  terms,  T6j. 

2.  What  part  of  |  is  -^  ? 

3        7  _ .  3        §_3  We    divide    r3g   by   J   by   inverting   the 

16       8  ~  16       7"    14      divisor  of  |  and  multiplying.     The  result 
2  shows  that  r\  is  fa  of  |. 

What  part  of 

3.  90  is  16?  6.   |  is  |?  9.   4  is  31? 

4.  120  is  50?  7.   lis^?  10.    13|islf? 

5.  200  is  18?  8.   \l  is  if?  li.    12|  is  If? 

12.  250  pupils  belong  to  a  school,  and  only  128  are 
present.     What  part  of  the  whole  number  is  present? 

13.  One  year  the  population  of  a  city  was  220,000,  and 
the  next  year  250,000.  What  fraction  of  the  second  year's 
population  was  the  first  year's? 

14.  The  product  of  two  numbers  is  29,160,  and  one  of  the 
numbers  is  27.     What  part  of  the  other  number  is  27? 


FRACTIONAL    RELATIONS  77 

Finding  a  number  when  a  fractional  part  of  it  is  given. 

l.    If  |  of  a  number  is  30,  what  is  the  number? 

If  three  fourths  of  the  number  is  30,  one  fourth  of  the  number  is  one 
third  of  30,  or  10,  and  four  fourths  of  the  number,  or  the  whole  number, 
is  4  x  10,  or  10.     Hence,  30  is  |  of  40. 

Written  Work 

1.  360  is  T6y  of  what  number  ? 

i  if  aon         en  Since  36°  is  rV  0T  a  number, 

TV  of  the  number  =  \  of  350,  or  60  ,  .    .  .  .  . 

J!    ,   ,  ,  ,„  _,,  „v  A-  of  it  is  1  of  360,  or  60,  and  H 

j  I  ot  the  number  =  17  x  00,  or  1020  TI  ..  .    , ,  " ,  .,„.         .      '  17 

17  of  it  is  V  oi  »360,  or  1020. 

2.  If  |  is  |  of  a  number,  what  is  the  number  ? 

Since  £  of  the  number  is  J, 
\  of  the  number  =  \  of  |,  or  57¥,  £  of  it  is  \  of  |,  or  ^V-  aQd  ?  of 

|  of  the  number  =  Ix  27?  =  |f,  or  li      the   number    is   1  x  27?,  which 


equals  §£,  or  1\. 

Find  the  number  of  which : 

3.    84    is  |           5.    3|    is  I 

7      -Z      is  -L 
/.      9      it>  16 

4.    196isT4T        6.    12|isi§ 

0       1  2  jo  6 
8.      Tg    1»   y 

9-     Hi8H 

10.   5fis^ 

11.  If  T93  of  a  man's  salary  is  $900,   what  is  his  salary  ? 

12.  A  man  lost  in  speculation  $2700,  which  was  -j3g  of  his 
entire  fortune.     What  was  his  fortune? 

13.  If  I.]-  of  the  number  of  books  in  a  library  is  9922, 
how  many  books  are  there  in  the  library  ? 

14.  There  are  30,205  women  in  a  certain  town,  which  is 
y7^  of  the  number  of  men.     How  many  men  are  there  ? 

15.  An  author  spent  $2100  for  a  piece  of  property,  which 
was  y7^  of  what  he  was  paid  for  a  novel.  How  much  did 
lie  receive  for  the  novel? 


78  FRACTIONS 

REVIEW  OF  FRACTIONS 

1.  |  of  30  is  f  of  what  number  ? 

2.  If  6  is  added  to  both  terms  of  the  fraction  f,  will  the 
value  be  increased  or  diminished,  and  how  much  ? 

3.  Change  iff  to  its  lowest  terms. 

4.  The  sum  of  two  numbers  is  43^.  One  of  the  num- 
bers is  18|.     What  is  the  other  ? 

5.  If  51  tons  coal  cost  $28.27,  find  the  cost  of  12§  tons. 

6.  If  2£  acres  of  land  cost  $110,  how  much  will  12| 
acres  cost  at  the  same  rate  ? 

7.  The  dividend  is  165,  and  the  quotient  is  6|.  What 
is  the  divisor  ? 

8.  Five  tubs  of  butter  contain,  respectively,  27^  lb., 
30|  lb.,  24  Jg  lb.,  32|  lb.,  and  34|  lb.  How  many  pounds 
are  there  in  the  five  tubs  ? 

9.  Multiply  the  sum  of  §  and  f  by  their  difference. 

10.  If  10  men  can  build  a  wall  in  35  days,  how  long  will 
it  take  25  men  to  do  the  work  ? 

11.  There  are    27 1\  square  feet  in  1  square  rod.     How 
many  square  rods  are  there  in  43560  square  feet  ? 

12.  If  a  man  travels  2|-  miles  in  f  of  an  hour,  at  the  same 
rate  how  far  could  he  travel  in  1\  hours  ? 

13.  A  man  owning  -^  of  a  mine  sold  his  interest  for 
$48700.     Find  the  value  of  the  mine  at  that  rate. 

14.  Find  the  difference  between  1\  x  3|  and  2\  -4-  3|. 

15.  A  merchant  owned  f  of  a  store,  and  sold  |  of  his  share 
for  $5760.     Find  the  value  of  the  whole  store  at  that  rate. 

16.  How  much  will  18000  stamped  envelopes  cost  at 
$21^  per  thousand  ? 


REVIEW  OE    FRACTIONS  70 

17.  When  oysters  yield  1{  gallons  to  the  bushel,  how 
many  bushels  will  be  required  to  till  a  10-gallon  tub  ? 

18.  One  buyer  offered  |  of  the  cost  of  a  property,  another 
|  of  the  cost.  The  difference  in  their  offers  was  $186.  Find 
the  cost  of  the  property. 

19.  Find  the  cost  of  18  yards  of  cloth  if  3|  yards  cost  $9. 

20.  A  clothier  paid  $180  for  12  suits  of  clothing,  and 
sold  them  at  $19|-  a  suit.     How  much  did  he  gain  ? 

21.  E,  who  owns  §  of  a  factory,  sells  |  of  his  share  for 
$3560.     What  is  the  value  of  the  factory  ? 

22.  What  is  the  distance  from  Pittsburg  to  Philadelphia 
if  |  of  the  distance  is  265^  miles  ? 

23.  The  product  of  two  fractions  is  | ;  one  is  ^,  what  is 
the  other  ? 

24.  If  C's  wages  are  $3|  a  day,  and  his  daily  expenses 
$1|,  how  many  days  must  he  labor  to  save  $28  ? 

25.  A  traveler  walked  25|  miles  the  first  day,  15|  miles 
the  second  day,  19|  miles  the  third  day,  20|  miles  the  fourth 
day,  and  22|  miles  the  fifth  day.  How  far  did  he  travel  in 
the  5  days,  and  what  was  the  average  rate  per  day  ? 

26.  A  field  is  40|  rods  long,  which  is  f  of  its  width. 
What  is  its  width  and  what  is  the  distance  around  the  field  ? 

27.  Find  the  cost  of  10A  cords  of  wood  at  $3  a  cord,  and 
8|  cords  at  $4  a  cord. 

28.  If  12|  bushels  of  apples  cost  $5,  how  much  will  15| 
bushels  cost  ? 

29.  A  farmer  raised  22f>  bushels  of  potatoes.  He  sold 
| of  them  to  one  merchant,  and  \  of  the  remainder  to  another. 
Find  the  number  of  bushels  he  had  left. 

30.  Reduce  \%  to  a  fraction  whose  denominator  is  320. 

lb 


80  FRACTIONS 

31.  Find  the  value  of  a  mill  if  f  of  f  of  it  is  worth  13750. 

32.  If  %  the  trees  in  an  orchard  are  peach  trees,  |  apple 
trees,  %  cherry  trees,  and  the  remaining  21,  plum  trees,  how 
many  trees  are  there  in  the  orchard  ? 

33.  What  number  is  it  whose  f  exceeds  its  §  by  40  ? 

34.  Divide  into  5- equal  parts  the  product  of  the  sum  and 
difference  of  1^  and  1|. 

35.  A  real  estate  dealer  sold  some  lots  for  §12360,  gain- 
ing 1  of  the  cost.     If  he  had  sold  them  for  $10500,  would  he 

&    5 

have  gained  or  lost,  and  how  much  ? 

36.  A  piece  of  land  was  sold  at  $  90  an  acre,  which  was  a 
gain  of  |  of  the  cost.    How  much  did  the  land  cost  per  acre  ? 

37.  My  board  and  room  cost  $32  per  month.  What  does 
each  cost  if  §  of  the  cost  of  the  room  equals  §  of  the  cost  of 
the  board  ? 

38.  A  father  left  $30000  to  his  two  children,  giving  the 
daughter  |  as  much  as  the  son.  What  was  the  share  of 
each? 

39.  The  owner  of  %  of  a  mill  sold  |  of  his  share  for  $4800. 
How  much  at  this  rate  would  a  man  who  owns  ^  of  the  mill 
get  for  23o  of  his  share? 

40.  One  fourth  of  a  certain  number  minus  3|  equals  -fa. 
What  is  the  number  ? 

41.  A  carpenter,  working  9|  hours  a  day,  built  a  shed  in 
16  days.  How  many  hours  a  day,  at  the  same  rate,  must  he 
work  to  build  it  in  18  days? 

42.  A  merchant  sold  10  dozen  hats  of  a  certain  kind  at 
$2.75  each,  and  a  number  of  dozens  of  another  kind  at  $2 
each,  receiving  $474  for  all.  How  many  dozen  did  he  sell 
at  $  2  each  ? 


REVIEW  OF   FRACTIONS  81 

43.  A  man  engaging  in  trade  lost  |  of  the  money  invested, 
then  gained  $495,  after  which  he  had  $2551.  How  much 
was  his  capital  at  first  ? 

44.  Simplify  ^  +  (£+1). 

5    Ui    9 

45.  A  hardware  merchant  bought  a  bill  of  hardware  at 
auction  for  \%  of  its  value,  and  retailed  it  for  f  of  its  value. 
If  his  gain  was  $48.75,  how  much  did  he  pay  for  it? 

46.  A  boy  bought  lemons  at  the  rate  of  4  for  5  cents,  and 
sold  them  at  the  rate  of  3  for  5  cents.  If  he  made  $6  in  2 
weeks  of  6  days  each,  what  were  his  daily  average  sales  ? 

47.  A  path  leading  to  the  top  of  a  hill  has  a  rise  of  9 
inches  in  90  feet.  What  is  the  elevation  of  the  hill  in  feet, 
if  the  path  is  f  of  a  mile  long  ? 

48.  A  teacher  taught  8*  months,  and  after  spending  f  of 
his  salary  for  board  had  left  $204.  How  much  did  he  earn 
per  month? 

49.  Divide  §  of  9  by  A  of  8|. 

50.  Two  men,  A  and  B,  each  bought  farms,  A's  farm  cost- 
ing 2|  times  as  much  as  B's.  Find  the  cost  of  each,  if  both 
cost  $58,000. 

51.  Divide  §  of  |  of  |  of  3|  by  f  of  ^  of  8^. 

52.  A  ship  is  worth  $120000,  and  the  owner  of  f  of  it  sells  \ 
of  his  share.     Find  the  value  of  the  part  he  has  remaining. 

53.  Find  the  value  of  (18|  -  |)  -  (20^  - 1$). 

54.  I  purchased  160  acres  of  land  at  $60  an  acre,  and  sold 
|  of  it  at  $70  an  acre.  Find  the  number  of  acres  I  had  left, 
and  my  gain  on  the  number  of  acres  sold. 

55.  A  real  estate  agent  bought  land  for  $7200,  and  sold  it 
so  as  to  gain  ^  of  the  cost.  If  the  gain  was  $6  per  acre, 
how  many  acres  did  he  buy  ? 

HAM.    COMPL.    ARITH.  — O 


82  FRACTIONS 

56.  A  man  paid  §  of  his  indebtedness  the  first  year,  §  of 
the  remainder  the  second  year,  f  of  what  then  remained  the 
third  year,  when  he  found  that  he  still  owed  $  1296.  Find 
the  amount  he  owed  at  first. 

57.  If  a  man  can  do  a  piece  of  work  in  6|  days  by  work- 
ing 9  hours  a  day,  how  long  will  it  take  him  to  do  it, 
working  8  hours  a  day  ? 

58.  Mr.  Williams  has  ^  of  his  money  in  government  bonds, 
|  in  the  bank,  and  $ 520  in  cash.     How  much  is  he  worth  ? 

59.  A  real  estate  agent  bought  2  houses ;  his  income 
from  the  one  was  $480,  which  was  |  of  the  income  from  the 
other.     How  much  was  his  income  from  both  houses  ? 

60.  Four  brothers  agreed  to  pay  the  mortgage  on  their 
father's  farm.  The  first  payment  made  was  ^  of  the  mort- 
gage, the  second  ^  of  the  remainder,  and  the  third  |  as  much 
as  the  first  and  second.  If  the  difference  between  the  first 
and  third  payments  was  $300,  how  much  was  the  mortgage? 

61.  A  merchant  bought  250  barrels  flour  at  $4.80  per 
barrel.  He  sold  10  barrels  which  were  damaged  for  |  of 
the  cost.  On  the  sale  of  150  barrels  he  gained  15  cents  per 
barrel.  If  his  total  gain  was  $28.50,  at  what  price  did  he 
sell  the  remaining  number  of  barrels  ? 

62.  A  merchant  buys  36  pairs  men's  shoes,  at  $2^  per  pair ; 
24  pairs  women's  shoes,  at  $1|  per  pair;  and  30  pairs  slippers, 
at  $|  per  pair.     What  is  the  amount  of  his  bill  ? 

63.  If  the  men's  shoes  in  example  62  are  sold  for  $3 
per  pair,  the  women's  shoes  for  $2|  per  pair,  and  the  slip- 
pers for  $1|  per  pair,  how  much  does  the  merchant  make  ? 

64.  A  cubic  foot  of  water  weighs  62|  pounds.  A  barrel 
contains  about  4*  cubic  feet.  Find  the  weight  of  a  barrel 
of  water. 


REVIEW   OF    FRACTIONS  83 

65.  A  student,  in  a  half  year  at  college,  spent  his  money 
as  follows:  tuition,  |50;  books,  $9|  ;  18  weeks'  boarding,  at 
$2|  per  week;  incidental  expenses.  $41|.  What  were  his 
expenses  for  the  half  year? 

66.  T9Y  of  a  barrel  of  oil,  containing  51  gallons,  was  sold 
at  13  cents  per  gallon;  the  remainder  of  the  barrel  at  14 
cents  a  gallon.  If  the  oil  cost  11|  cents  per  gallon,  what 
was  the  gain  ? 

67.  A  merchant  bought  a  stock  of  goods  for  16000.  He 
sold  |  of  it  at  a  gain  of  l  of  the  cost.  \  of  it  at  a  gain  of  \  of 
the  cost,  and  the  remainder  at  a  loss  of  \  of  the  cost.  How 
much  did  he  gain  or  lose  ? 

68.  A  hall  is  21f  feet  long  and  10]  feet  wide.  At  8£ 
cents  per  foot,  how  much  will  it  cost  to  put  a  molding 
around  this  hall? 

69.  Find  the  perimeters  of  each  of  five  rooms,  the  dimen- 
sions being  as  follows  :  221  ft.  x  16  ft.,  14f  ft.  x  15*  ft., 
12§  ft.  x  17  ft.,  181  ft.  x  lof  ft.,  m  ft.  x  24  ft. 

70.  From  a  certain  number  18|  +  '2~^  was  subtracted, 
leaving  a  remainder  of  9T5g.     What  was  the  number? 

71.  From  New  York  to  Chicago  by  the  Baltimore  and 
Ohio  railroad  the  distance  is  1052  miles.  From  Chicago  to 
El  Paso  by  the  Santa  Fe  railroad  it  is  1630  miles,  and  from  El 
Paso  to  Mexico  City  by  the  Mexican  Central  railroad  it  is 
1224^  miles.  What  is  the  distance  from  New  York  to 
Mexico  City,  and  how  long  would  such  a  journey  take, 
traveling  31 1  miles  per  hour  ? 

72.  A  freight  train  runs  from  Kansas  City  to  St.  Louis, 
288  miles,  traveling  16  miles  per  hour.  How  long  does  it 
take  it  to  make  the  trip?  How  long  would  it  take  a  pas- 
senger train,  running  \  as  fast,  to  make  the  same  trip? 


PROBLEMS   FOR  ANALYSTS 

Pupils  should  be  taught : 

(1)  To  express  themselves  accurately  and  rapidly ;  (2)  to 
do  this  work  without  the  aid  of  pencil  and  paper  ;  (3)  to 
give  clear  analytic  statements  in  the  solution  of  a  problem. 

1.  The  coal  for  the  school  buildings  in  a  certain  town 
cost  $94.50.     How  many  tons  were  purchased  at  $3  per  ton  ? 

2.  A  shoe  dealer  buys  shoes  at  $21  per  dozen  pairs  and 
retails  them  at  $2.50  a  pair.  How  much  does  he  gain  on 
each  pair  ? 

3.  A  laborer  earns  $18  in  12  days.  At  that  rate  how 
much  can  he  earn  in  80  days  ? 

4.  What  is  f  of  f  of  24  ? 

5.  A  lady  buys  10  yards  of  ribbon  and  uses  6|  yards. 
What  part  of  the  ribbon  has  she  left  ? 

6.  If  eggs  are  bought  at  the  rate  of  4  dozen  for  $1.08 
and  sold  at  30  cents  per  dozen,  what  will  be  the  gain  on  3 
dozen  ? 

7.  A  man  buys  a  farm  of  102  acres  and  divides  it  into 
lots  of  6  to  the  acre.  How  many  lots  are  there  if  £  of  the 
farm  is  laid  out  in  streets  ? 

8.  How  many  sheep,  at  $5  per  head,  may  be  purchased 
with  the  money  from  the  sale  of  10  head  of  cattle  at  $42  per 
head? 

9.  A  contractor  buys  8000  bricks  at  $12.50  per  thousand. 

Find  the  amount  of  his  bill. 

84 


PROBLEMS    FOR    ANALYSIS  85 

10.  If  I  pay  6  cents  for  the  use  of  §1  for  one  year,  how 
much  should  I  pay  for  the  use  of  §150  for  -  years/ 

11.  If  I  buy  goods  at  $1.37  per  yard  and  sell  them  at 
11.50  per  yard,  how  much  do  I  gain  on  12  yards? 

12.  A  boy  earns  75  cents  per  day  and  pays  f  of  his  wages 
for  board.     At  that  rate  how  much  can  he  save  in  26  days  ? 

13.  My  father  pays  §252  per  year  rent.  How  much  is 
that  per  month  ? 

14.  A  lady  purchased  2  handkerchiefs  at  35  cents  each  ; 
6  yards  of  ribbon  at  12  cents  per  yard ;  6  yards  of  cloth  at 
§1.12  per  yard.  How  much  change  should  she  receive  from 
a  ten-dollar  bill  ? 

15.  A  man  buys  a  farm  for  §2000  and  pays  |  of  the  cost, 
giving  his  note  for  the  balance.  For  how  much  does  he 
give  his  note  ? 

16.  A  farmer  buys  fertilizer  at  §28  per  ton  and  retails 
it  at  §1.90  a  hundred  pounds.  How  much  does  he  gain  on 
35  tons  ? 

17.  At  16  cents  per  pound,  how  many  pounds  of  steak 
does  a  woman  get  if  the  amount  of  the  purchase  is  83  cents  ? 

18.  A  huckster  bought  6|-  pounds  of  butter  at  16  cents 
per  pound,  and  6|  dozen  eggs  at  18  cents- per  dozen.  How 
much  did  he  pay  for  both? 

19.  A  huckster  buys  chickens  at  8^  cents  per  pound  and 
sells  them  at  12 1  cents  per  pound.  How  many  pounds  must 
he  purchase  and  sell  in  order  to  gain  §25? 

Solution. — On  each  pound  he  gains  4£  cents. 
To  gain  $1  he  must  sell  24  pounds. 
To  gain  $25  he  must  sell  25  times  24  pounds,  or  600 
pounds. 

20.  A  street  car  conductor  earns  23  ^  cents  per  hour. 
How  much  does  he  earn  in  10  hours  ? 


86  PROBLEMS   FOR   ANALYSIS 

21.  If  the  conductor  averages  10  hours  per  day,  how 
much  will  he  earn  in  80  days  ? 

22.  If  a  box  of  40  dozen  oranges  is  purchased  for  $5 
and  retailed  at  40  cents  a  dozen,  what  is  the  entire  gain  ? 

23.  What  fraction  of  a  gallon  is  a  pint  ?  a  gill  ?  a  quart  ? 

24.  A  man  sold  |  of  his  farm  for  $1800.  At  the  same 
rate,  how  much  would  he  receive  for  the  whole  farm  ? 

Solution.  —  §  of  the  amount  received  for  the  farm  =$1800. 

£  of  the  amount  received  for  the  farm  =  \  of  $1800,  or 

$900. 
f ,  or  the  amount  received  for  the  farm  =  3  times  $  900, 

or  $2700. 

25.  In  a  certain  school  there  are  40  pupils  in  the  grammar 
grade,  which  are  f  of  the  number  in  the  intermediate  grade. 
How  many  pupils  are  there  in  both  grades  ? 

26.  A  man  sold  a  piano  for  $360,  which  was  |  of  what  it 
cost  him.     How  much  did  it  cost  him  ? 

27.  There  are  112  cubic  feet  in  |  of  a  cord  of  wood.  How 
many  cubic  feet  are  there  in  1  cord  ? 

28.  A  farmer  sold  |  of  his  farm  for  $1521.  At  that  rate, 
what  was  the  value  of  §  of  the  farm  ? 

29.  There  are  198  cubic  inches  in  $  0f  a  gallon.  How 
many  cubic  inches  are  there  in  2  gallons  ? 

30.  If  |  of  a  ton  of  hay  costs  $16,  how  much  will  2|  tons 
cost? 

31.  A  lady  paid  84  cents  for  |  of  a  yard  of  silk.  At  the 
same  rate,  how  much  would  she  pay  for  |-  yard  ? 

32.  If  ^  of  an  acre  produces  160  bushels  of  potatoes,  how 
many  bushels  will  an  acre  produce  ? 

33.  A  man  saves  $220,  which  is  f  of  his  yearly  salary. 
What  is  his  yearly  salary? 


PROBLEMS   Foil   ANALYSIS  ST 

34.  If  it  takes  4  men  9  days  to  do  a  piece  of  work,  how 
long  will  it  take  6  men,  at  the  same  rate,  to  do  the  work  ? 

35.  If  |  of  a  farm  is  valued  at  $  1240,  what  is  the  value  of 
^  of  the  farm  ? 

36.  A  lady  spends  §  of  her  income  for  hoard,  and  1  of  the 
remainder  for  clothes  and  travel.  If  she  saves  $160  per 
year,  what  is  her  income  ? 

37.  A  farmer  has  600  bushels  of  wheat,  which  is  \  of  | 
of  what  his  neighbor  has.  How  many  bushels  has  his 
neighbor  ? 

38.  A  house  was  sold  for  11800,  which  was  §  of  its  cost. 
What  was  the  loss  ? 

39.  If  20  men  can  dig  a  ditch  in  25  days,  how  long  will  it 
take  5  men  ? 

40.  A  farmer  sold  36  head  of  cattle,  which  was  6  more 
than  ^  of  all  he  owned.      How  many  had  he  remaining  ? 

41.  If  a  man  works  |  of  a  day  and  receives  $1.50,  how 
much  should  he  receive  for  f  of  a  day  ? 

42.  I  purchased  an  overcoat  for  $45,  and  found  I  had  %  of 
my  money  left.     How  much  had  I  at  first  ? 

43.  James  and  John  have  together  $40,  and  John  has 
seven  times  as  much  money  as  James.  How  much  does 
each  have  ? 

Solution.  —  Once  James's  money      =  James's  money. 
7  times  James's  money  =  John's  money. 


8  times  James's  money  =  amount  of  both,  or 

Once  James's  money      =  $5. 

7  times  James's  money  =  8-35,  or  John's  money. 

44.   There  are  two  numbers  whose  sum  is  40;  one  number 

is  A  of  the  other.     What  are  the  numbers? 


88  PROBLEMS   FUR  ANALYSIS 

45.  A  man  invests  \  of  his  money  in  a  mill,  |  in  a  farm, 
and  the  remainder,  which  is  $900,  he  deposits  in  a  bank. 
How  much  is  he  worth  ? 

46.  A  town  has  3000  people.  The  number  of  pupils  in 
the  school  is  \  of  the  remaining  population.  How  many 
pupils  are  there  in  the  school  ? 

47.  In  a  farm  of  500  acres  the  woodland  is  §  of  the  cleared 
land.     How  many  acres  are  there  of  each  ? 

48.  A  miller  has  360  bushels  of  wheat,  §  of  the  number 
of  bushels  of  wheat  equals  |  of  the  number  of  bushels  of 
corn.     How  much  is  the  corn  worth  at  50  cents  per  bushel? 

49.  If  |  of  a  clerk's  salary  for  the  year  is  $800,  how  much 
is  I  of  his  salary  ? 

50.  |  of  21  is  -^  of  what  number  ? 

51.  §  of  20  is  T43  of  what  number  ? 

52.  |  of  I  of  a  number  is  16.     What  is  the  number  ? 

53.  I  of  C's  farm  equals  ^  of  D's,  and  C  has  100  acres. 
How  many  acres  has  D  ? 

54.  There  are  two  numbers:  §  of  the  first  is  f  of  the 
second.     The  first  number  is  18.     What  is  the  second  ? 

55.  A  and  B  agree  to  do  a  piece  of  work  for  $80.  If  A 
works  7  days  and  B  9  days,  how  much  should  each  receive? 

Suggestion.  —  Together  they  work  16  da.  Hence,  A  should  receive 
r\  of  $  80,  and  B  T9S  of  $  80. 

56.  Sarah  earns  $10  a  week,  and  ^  of  what  Sarah  earns  is 
§  of  what  Edna  earns.     How  much  does  Edna  earn  ? 

57.  |  of  T3^  of  160  is  T8T  of  what  number  ? 

58.  If  |  of  |  of  a  farm  costs  $2500,  how  much  does  the 
farm  cost  ? 


PROBLEMS   FOR   ANALYSIS  80 

59.  I  of  my  money  is  invested  in  coal  land,  \  of  the 
remainder  in  building  lots,  and  the  remainder,  which 
amounts  to  $800,  is  in  the  bank.  How  much  have  I 
invested  in  coal  lands  ? 

60.  A  man  sold  a  horse  for  8120,  winch  was  \  less  than 
the  horse  cost  him.     Find  the  cost. 

61.  If  24  is  |  of  a  number,  21  is  what  part  of  that  number  ? 

62.  I  spend  \  of  my  monthly  salary  for  board  and  room, 
\  of  the  remainder  for  clothing,  and  save  the  remainder, 
which  is  $20.     What  is  my  salary? 

63.  If  f  of  a  piece  of  work  can  be  done  in  9  days,  how  long 
will  it  take  to  complete  the  work  after  f  has  been  done  ? 

64.  By  selling  land  at  $120  an  acre,  I  gain  J  of  the  cost. 
Find  the  cost. 

65.  If  |  of  the  value  of  a  farm  is  $000,  what  is  the  value 
of  |  of  the  farm  ? 

66.  If  4|  tons  of  coal  cost  $27,  how  much  will  3  tons  cost  ? 

67.  What  is  the  difference  between  \  of  \  and  §  of  1  ? 

68.  If  I  can  do  a  piece  of  work  in  7  days,  what  part  can  I 
do  in  1  day?  in  3  days?  in  §  of  a  day?  in  1|  days? 

69.  A  fruit  grower  sold  200  bushels  of  apples,  which  was 
A  of  his  crop.  How  much  did  he  realize  from  the  sale  of 
his  crop  at  $1.20  per  bushel  ? 

70.  An  heir  gets  f  of  an  estate  and  invests  f  of  his  share, 
and  still  has  $1600.     What  is  the  value  of  the  estate  ? 

71.  A  tank  holds  120  gal.  and  is  f  full.  §  of  the  quantity 
is  drawn  off.     How  many  gallons  will  it  take  to  fill  the  tank  ? 

72.  One  man  bids  ^  of  tlie  cost  of  an  article'  another  man 
bids  §  of  the  cost  of  the  article.  The  difference  between 
their  bids  is  70  cents.     Find  the  cost  of  the  article. 


DECIMAL   FRACTIONS 

1.  What  is  the  largest  common  fractional  unit  ? 

2.  Show  that  an  integral  unit  may  be  divided  into  any 
number  .of  fractional  units. 

3.  Name  the  different  fractional  units  from  \  to  2V  in  order 
of  their  size. 

4.  What  fractional  unit  divides  the  integral  unit  into  10 
equal  parts  ?     into  100  equal  parts  ?    into  1000  equal  parts  ? 

The  divisions  of  an  integral  unit  into  lOths,  lOOths, 
lOOOths,  etc.,  are  called  decimal  divisions. 

There  are  three  ways  by  which  decimal  divisions  may  be 
expressed : 

(1)  by  words,  as  nine  tenths ; 

(2)  by  common  fractions,  as  j9q,  y|7  ; 

(3)  by  decimals,  as  .9,  .75. 

A  decimal  fraction  is  any  number  of  lOths,  lOOths,  lOOOths, 
etc.  of  an  integral  unit.  When  expressed  after  a  decimal 
point  and  without  a  written  denominator,  it  is  usually  called 
a  decimal. 

A  decimal  point  is  a  period  placed  after  ones'  place  and 
before  tenths'  place. 

5.  What  is  the  largest  decimal  unit?  the  second  largest? 
the  third  largest? 

In  any  decimal  system  10  x  1  unit  in  any  place  =1  unit  of 
the  next  higher  place. 

6.  Show  that  United  States  money  is  a  decimal  system. 

90 


NOTATION    AND   NUMERATION  91 

NOTATION    AND    NUMERATION    OF    DECIMALS 

1.  Since  the  first  decimal  division  of  an  integral  unit  is 
tenths,  what  is  the  first  place  to  the  right  of  the  decimal  point? 

2.  What  is  the  second  place  called  ?  the  third  place  ? 

3.  Five  tenths  is  written  .5  ;  five  hundredths  is  written 
.05  ;  five  thousandths  is  written  .005,  etc.  Write  7  tenths, 
6  hundredths,  8  thousandths. 

4.  Express  decimally  ^,  ^,  TT^  iooo'  Too'  Tooo- 
Every  decimal  contains  as  many  decimal  places  as  there  are 

naughts  in  the  denominator  of  the  equivalent  fraction. 

Table  of  places  and  names  of  integral  and  fractional  units : 


CO 

a 
© 


s 
H 


a 
o 


5     3 


CO 

.3 

CO 

*j 

13 

-a 

a 

GO 

3 

d 

GO 

CO 

S 

CO 

+3 

CO 

3 

CO 

J3 

O 

a 

.« 

CO 

J3 

.4 

c« 

CO 

CO 

tn 

o 

- 

-a 

i 

so 

T3 

3 

a 

T3 

H 

•C 

— * 

13 

+J 

£3 

CO 

o 

c* 

CO 

eS 

CO 

co 

=s 

o 

CO 

2 

•r* 

"2 

— 

1 

CO 

C5 

-5 

K 

CO 

S 

'3 

XI 

■o 

CO 

© 

"3 

•3 

.2 

a 

8 

co 

H 

X 

a 

O 

co 
Q 

CO 

H 

3 

S 

J3 

r£ 

8 

§ 

CO 

H 

5 

7 

8 

4 

5 

5 

• 

0 

0 

7 

4 

8 

9 

8 

5.  In  .555  what  figure  stands  for  tenths?  for  hun- 
dredths ?   for  thousandths  ?     It  is  read  555  thousandths. 

6.  Is  the  decimal  point  named  in  reading  a  decimal  ? 
Observe  that  the  decimal  is  read  as  an  integer  and  that 
the  last  figure  is  given  the  required  denomination. 

Read : 

7.  .25  li.  .101  15.  .60745 

8.  .05  12.  .0045  16.  .678705 

9.  .005  13.  .4045  17.  .0065 
10.    .375  14.  .0002  18.  .60005 


92  DECIMAL  FRACTIONS 

19.  50.0745  is  read  50  and  745  ten-thousandths.  How 
are  both  the  integer  and  the  decimal  read  ?  How  is  the  deci- 
mal point  read  ?  What  name  is  given  to  the  last  decimal 
place  ? 

20.  When  is  the  decimal  point  read  ?    When  is  it  not  read  ? 

21.  What  determines  the  value  of  any  figure  in  a  decimal  ? 

22.  In  writing  .5,  .45,  .075,  .0075  as  common  fractions, 
what  figure  in  each  decimal  tells  us  the  size  of  the  denomi- 
nator ? 

A  mixed  decimal  is  a  whole  number  and  a  decimal ;  as, 
4.625. 

23.  What  number  in  a  mixed  decimal  is  always  read  first? 

24.  How  do  the  number  of  places  in  any  decimal  compare 
with  the  number  of  naughts  in  the  denominator  when  the 
decimal  is  expressed  as  a  common  fraction  ? 

Read : 

25.  45.075  28.        72.003745 

26.  50.3007  29.    1001.1001 

27.  290.25387  30.      794.3085 

34.  5  thousandths  calls  for  how  many  decimal  places? 
What  part  of  the  decimal  (5  thousandths)  stands  for  the 
numerator  of  the  fraction?  what  part  of  this  decimal  stands 
for  the  denominator? 

35.  Name  the  numerator  and  the  denominator  in  the  fol- 
lowing decimals:  .05,  .0006,  .000025,  .045. 

In  writing  a  decimal  write  the  numerator,  and  point  off 
from  the  right  as  many  decimal  places  as  there  are  naughts 
in  the  denominator. 


31. 

.00875 

32. 

.008090 

33. 

2.004890 

DOTATION    AND   NUMERATION  93 

Written  Work 
Write  : 

1.  34  hundredths. 

2.  675  ten-thousandths. 

3.  16  and  75  millionths. 

4.  400  and  45  thousandths. 

5.  6006  and  66  ten-thousandths. 

6.  89  and  5  thousandths. 

7.  Seven  hundred  forty-six  ten-thousandths. 

8.  Nine  hundred  and  84  millionths. 

9.  5  million  9  and  4  hundred  9  ten-millionths. 

10.  5095  millionths. 

11.  8  and  17  ten-thousandths. 

12.  125  millionths. 

13.  896  and  301  hundred-thousandths. 

14.  One  thousand  and  one  thousandth. 

15.  18051  and  957  thousandths. 

16.  97  and  3  ten-thousandths. 

17.  9864  millionths. 

18.  '2135  and  32  millionths. 

19.  One  and  one  millionth. 

20.  One  million  and  one  tenth. 

21.  90  thousand  and  71  thousandths. 

22.  1830  and  11684  hundred-thousandths. 

23.  429  thousand  and  46  ten-thousandths. 

24.  7035  and  97  hundredths. 

25.  67375  and  35  hundred-thousandths. 

26.  5815  hundred-thousandths. 

27.  375  and  69  thousandths. 


94  DECIMAL   FRACTIONS 

28.  419863  and  23456  millionths. 

29.  81  and  921  hundred-thousandths. 

30.  2986  and  298643  ten-millionths. 

31.  3020  and  302  hundred-thousandths. 

32.  70  and  7  hundredths. 

33.  8  thousand  and  8  thousandths. 

34.  645  million  and  9  millionths. 

COMPARISON  OF  COMMON  FRACTIONS  AND  DECIMALS 

2.  Then  observe  that  5  tenths  =  50  hundredths  =  500 
thousandths.     .5  =  .50  =  .500. 

3.  50  hundredths  may  be  written  .50,  or  .500.  Does 
adding  naughts  to  the  right  of  a  decimal  change  the  value  of 
the  decimal? 

4.  What  is  the  difference  in  value  between  $.5  and  1.50? 
In  writing  decimal  parts  of  a  dollar,  we  always  write  two 
places  for  cents  even  if  the  last  place  is  a  naught. 

5.  Compare  in  value  \  and  T5^,  T5^  and  -^$q. 

6.  Does  canceling  the  same  number  of  naughts  from 
both  numerator  and  denominator  change  the  value  of  a 
fraction  ? 

7.  Since  .5  =  .50  =  .500,  does  canceling  naughts  from  the 
right  of  a  decimal  change  the  value  of  the  decimal  ? 

8.  Observe  that  canceling  naughts  from  the  right  of  a 
decimal  really  means  canceling  naughts  from  the  numerator 
and  the  denominator. 

ThuS,.50  =  ir.5P  =  l|. 


COMMON   FRACTIONS    AND    DECIMALS  95 

9.    .400  is  read  400  thousandths.     How  else  may  it  be 
read  ? 

10.    Is  the  unit  in  .4  the  largest  decimal  unit  in  which 
.400  can  be  expressed  ? 

Read  first  as  given,  then  as  if  the  naughts  at  the  right  of 
the  decimal  were  canceled  : 


11. 

.040 

13. 

.7500 

15. 

10.0057 

12. 

26.0050 

14. 

8.0090 

16. 

20.0900 

Changing  decimals  to 

common 

fractions. 

Write  as  common  fractions  and  change  to  lowest  terms  : 

l. 

.25 

3. 

.045 

5. 

.50 

7. 

.0025 

2. 

.7 

4. 

.025 

6. 

.75 

8. 

.0775 

9.    Give  the  steps  in  changing  a  decimal  to  its  fractional 
equivalent. 

A  complex  decimal  is  a  decimal  and  a  fraction  united; 
thus,  .16 1  is  read  16 1  hundredths. 

*      3==  100x3      300      6' 
10.    Explain  why  multiplying  both  terms  of  the  fraction 

i-^  bv  3  does  not  change  the  value  of  the  fraction. 
100     J  ° 

Change  to  common  fractions: 


11. 

.371 

15. 

.831 

19. 

•62£ 

23. 

lOl 

12. 

.41 1 

16. 

•  06£ 

20. 

•33£ 

24. 

.14f 

13. 

.66| 

17. 

.04  \ 

21. 

.31^ 

25. 

•58i 

14. 

.241 

18. 

.081 

22. 

•03£ 

26. 

.88J 

96  DECIMAL   FRACTIONS 

ADDITION  AND  SUBTRACTION  OF  DECIMALS 

1.  How   must   integers   be    written  before  they  can  be 
added  '?  subtracted  ? 

2.  What  change  must  be  made  in  \  and  |  before  they  can 
be  added  or  subtracted  ? 

In  adding  or  subtracting  decimals,  tenths  must  be  placed 
under  tenths,  hundredths  under  hundredths,  thousandths 
under  thousandths,  etc. 

Written  Work 

3.  Add  .8085  and  .005.     4.   Subtract  .005  from  .8085. 
.8085  .8085 

.005  .005 


.8135  .8035 

Add  as  indicated  and  test  : 

5.  6.  7.  8. 

9.        .45       +     72.5       +       8.557     +     87.       =    — 

10.  8.07       +       5.07     +       0.039     +       6.5     =    — 

11.  62.093  +  89.09  +  16.909  +  11.9  =  — 

12.  40.937  +  20.98  +  41.005  +  0(15  =  — 

13.  4-        +         +       =  — 

Subtract  examples  14  to  17  and  add  the  remainders  : 
14.  15.  16.  17. 

40.275  9.0098  219.75  28.7 

39.009  6.7849  8.95  12.5 

18.  +  +  +  =  — 
Add: 

19.  3.7  20.    .001  21.-   .65 
5.06           12.3  .001 
8.023          15.0248          10.1 
9.04           18.0149          25.004 


ADDITION   AND   SUBTRACTION  9' 


Add: 

22.    1.1 

23. 

120.2601 

24. 

36.15 

4.01 

230.81002 

9.00999 

1.0101 

.05673 

128.37 

5.055 

26. 

3.7 

27. 

16,08753 

25.  166.6 

.27 

185.057 

7.0425 

.0616 

127.0348 

28.318 

.010912 

216.253 

142.0101 

1.940054 

456.03456 

Add  : 

28.  12.015,  26.01102,  126.0592,  134.00876. 

29.  100.001,  9.99,  149.0492,  7.077. 

30.  2.2,  28.18,  140.027,  284.0295. 

31.  318.003,  33.33,  495.0485,  12.0012. 

32.  Find  the  weight  of  four  silver  bars  weighing  as  fol- 
lows :  15.75  pounds,  .125  pounds,  14.3125  pounds,  and 
16.875  pounds. 

33.  Find  the  number  of  acres  in  four  fields  containing, 
respectively,  4.125  acres,  .3125  acres,  8.8  acres,  and  9.85 
acres. 

34.  Find  the  sum  of  one  hundred  twenty-five  and  seven 
hundredths,  eighty-nine  and  two  hundred  thirty-five  thou- 
sandths, one  hundred  twenty-seven  ten-thousandths,  and 
sixteen  and  four  tenths. 

35.  A  farm  cost  * 4225.50;  stock,  $745.25;  buildings, 
■$1825.75;  and  implements,  $358.45.  What  was  the  total 
cost? 

36.  How  many  square  feet  are  there  in  four  floors 
measuring,  respectively,  245|  square  feet,  278|  square  feet, 
174.375  square  feet,  and  168.3125  square  feet? 

HAM.     COMPL.    A  KITH- 7 


98  DECIMAL  FRACTIONS 

Find  differences : 


37. 

.75 

.1825 

38. 

.3216 

.275 

39. 

4.205 

1.7856 

40. 

15. 

5.007 

41. 

38. 
18.276 

42. 

$45.67 
12.09 

43. 

1251 
87.432 

44. 

249| 
178.625 

45. 

230.4897 
116.5988 

46. 

100.001 
99.9 

47. 

1001.101 
900.909 

48. 

105.55 
79.067 

49. 

1.1 
.999 

50. 

5.05 
.6565 

51. 

8.25 
.0085 

52. 

1000.00 
999.99 

53.  (9.5- 2.25)  +  (15.28-12.056) +  (22.089- 19.063). 

54.  (11.001- 1.99)  +  (17.0107-14.014)  +  (29.3-23.2867). 

55.  The  difference  between  two  numbers  is  1001.101,  and 
the  greater  is  1101.011.     What  is  the  smaller  number? 

56.  A  is  35.875  years  old,  B  is  48.25  years  old,  and  C's 
age  is  25.5  years  less  than  the  age  of  A  and  B  combined. 
How  old  is  C  ? 

57.  To  the  sum  of  .808  and  80.8  add  their  difference. 

MULTIPLICATION  OF   DECIMALS 

1.  Multiply  .05  by  .5. 

2.  What  is  the  numerator  in  .05  ?  in  .5? 

3.  What  is  the  denominator  in  .05  ?  in  .5  ?     What  shows 
the  denominator  in  a  decimal  ? 

4.  Multiply  the  numerators  in  .5  x  .05  ;  thus,  5x5  =  25. 

5.  Multiply  the  denominators  in  .5x.05;  thus,  10x100 
=  1000. 

6.  Write  the  result  as  a  common  fraction ;  thus,  Tf -| ^ . 

7.  What  term  of  the  fraction  is  expressed  by  the  decimal 
point  ? 


MULTIPLICATION  99 

Observe  that  there  are  as  many  decimal  places  in  each  deci- 
mal as  there  are  naughts  in  the  denominator  of  the  equiva- 
lent common  fraction. 

Find  the  product  of  the  following  decimals  by  multiplying 
the  numerators  and  the  denominators,  separately,  and  ex- 
pressing the  result  as  a  decimal ;  thus, 

•04x-7=i^xii=iIro=-028 

9.    .2x.06  12.    .35x.05  15.    .02  x  .42 

10.  .04  x  .5  13.    .07  x  .05  16.    .06  x  .004 

11.  .25  x  .05  14.    .03  x  .02  17.    .05  x  .009 

The  product  of  two  decimals  contains  as  many  decimal  places 
as  the  sum  of  the  decimal  places  in  both  factors. 

Written  Work 

l.    Multiply  .25  by  5. 

fa\  5  x  5  hundredths  =  25  hundredths  or  2  tenths  and 

5  hundredths.     Write   the   5   in   hundredths'  place, 

•""  and   carry   the   2.     5x2    tenths  =  10    tenths;    10 

2.  tenths +  2  tenths  =  12  tenths,  or  1  aud  2  tenths. 


1.25  Hence,  5  x  .25  =  1.25. 

2.    Multiply  .26  by  .12. 

(h) 

cyo  1.   What  is  the  sum  of  the  decimal  places  in 

the  two  factors  ? 

2.   The  product,  then,  must  contain  how  many 


.12 


52  places? 

26 


.0312 
When  the  product  has  not  enough  decimal  places,  supply  the 
deficiency  by  prefixing  naughts. 


100  DECIMAL   FRACTIONS 

Find  products  : 

3.  .25  x  .22  20.  .1232  x  .961  37.  .4986  x  .086 

4.  .17x.28  21.  .2592x8  38.  .006x20 

5.  .027  x  .03  22.  65.65  x  .65  39.  38.2  x  .75 

6.  27  x  .12  23.  75.002  x  16.04  40.  .0045  x  .05. 

7.  .35x42  24.  275  x  .007  41.  9.876  x  .786 

8.  8.7x9.22  25.  .0018x720  42.  362.9  x  .0076 

9.  .085x50  26.  1500  x  .004  43.  119.8x2.74 
10.  .027  x  18  27.  124  x  .064  44.  20.08  x  .006 
li.  1.005  x  .011  28.  326  x  .096  45.  .375  x  2.027 

12.  26.8  x  34  29.  627  x  .78  46.  98.64  x  4.096 

13.  28.25  x  12  30.  246  x  .3  47.  .069  x  8.92 

14.  324.6  x  81  31.  29.4  x  .08  48.  6.34  x  2.34 

15.  39.10  x  18.4  32.  9.86  x  3.8  49.  12.34  x  .004 

16.  .0214  x  .016  33.  39.75  x  .27  50.  6.08  x  .0001 

17.  12.134  x. 0025  34.  8.708x6.8  51.  1.002x1.004 

18.  15.684  x  8  35.  368.9  x  8.5  52.  .05  x  .005 

19.  .1232  x  345  36.  2009  x  .006  53.  6.876  x  4.37 

54.  How  much  must  be  paid  for  85  acres  of  land  at 
$45.75  per  acre  ? 

55.  Three  brothers  divided  an  estate  worth  19600.  The 
first  received  .125  of  it,  the  second  .375  of  it,  and  the  third 
the  remainder.     How  much  did  each  receive  ? 

56.  A  contractor  furnished  2,626,000  bricks  at  $7.75  a 
thousand,  and  a  laborer  for  65  days  at  $2.75  a  day.  What 
was  the  amount  of  his  bill  ? 

57.  If  there  are  39.37  inches  in  a  meter,  how  many  inches 
are  there  in  12  meters  ?  how  many  yards  ? 


DIVISION  30] 

Multiplying  by  moving  the  decimal  point. 

1.  Multiply  6.385  by  10;   by  100  ;  by  100TT. 

10  x  6.385  =  63.85  1-  How  do  you  murtfpjj  a  ribjrnWi  6j  10? 

inn       a  oor       />oc  c  -.   How  may  you  multiply   it  decimal  b<' 

100  xb.38o  =  638.5     U)?  by  lu(),  by  U)()((, 

1000  x  6.38o  =  638o  3   How  is  the  Ya]ue  of  a  nuillber  affected 

by  moving  the  decimal  point  one  place  to  the  right?   two  places?  three 

places  ? 

Moving  the  decimal  point  one  place  to  the  right  multiplies 
the  number  by  10  ;  two  places  by  100  ;  three  places  by  1000. 

2.  Multiply  6.1234  by  10  ;  by  100  ;  by  1000. 

3.  Multiply  .0342  by  10  ;  by  100  ;  by  1000. 

4.  Multiply  1.3412  by  10;  by  100  ;  by  1000. 

DIVISION  OF  DECIMALS 
Dividing  a  decimal  or  a  mixed  decimal  by  an  integer. 

1.  Find  J  of  48  hundredths;  of  64  hundredths. 

2.  Find  \  of  .25;  of  .35;  .45;  .75. 

3.  Find  I  of  6  and  36  hundredths;  12  and  24  hundredths. 

4.  Find  1  of  12.36;  24.42;  48.06;  54.06. 

Observe  that  in  each  problem  a  decimal  or  a  mixed  decimal 
when  divided  by  an  integer  is  simply  separated  or  partitioned. 

Give  quotients  at  sight : 

5.  J  of  .16         9.    i  of  6.6  13.  6.42-6  17.  .006-5-3 

6.  iof.25       io.   J  of  8.08  14.  12.04-4  18.  .024-5-6 

7.  iof.08       li.   -J  of  10.10  15.  15.05-S-5  19.  .008-5-4 

8.  J  of  .04       12.    i  of  12.06  16.  24.18-5-3  20.  .105-5-5 


102  DECIMAL   FRACTIONS 

Written  Work 

l.    Divide  12t).685  by  15.  2.    Divide  174.44  by  28. 

_    1  379             How  many  times  is  15  con-  6.23 

15)20.685         tainedin20?    in  5.6  ?  in  1.18?  28)174.44 

15.                in  .135?  '     168' 

~~F~f>  In  practice  we  divide  as  in 

the  second  example,  placing  the  " 

•"              decimal  point   directly   above  56_ 

1.18           the  point  in  the  dividend,  be-  84 

1.05           fore  beginning  to  divide,  and  $4 
J35         dividing  as  in  integers. 

.135 


When  the  divisor  is  an  integer,  division  simply  separates  or  partitions 
the  dividend  into  equal  parts.  Thus,  ^  of  20  and  085  thousandths 
(20.085)  =  1  and  379  thousandths  (1.379). 

A  decimal  or  a  mixed  decimal  is  divided  by  an  integer  by 
'placing  a  decimal  point  above  or  below  the  decimal  point  in  the 
dividend,  before  beginning  to  divide,  and  dividing  as  in  the 
division  of  integers. 


3. 

96.16-4-8 

16. 

12.312-4-27 

4. 

849.6-^-6 

17. 

2.25-4-15 

5. 

72.84-^-12 

18. 

809.6-4-16 

6. 

22.5-15 

19. 

256.25-4-25 

7. 

80.96-4-16 

20. 

96.064-4-32 

8. 

2.5625  -f-  25 

21. 

7010.5-4-35 

9. 

.96064-4-32 

22. 

61.472-4-68 

10. 

701.05-4-35 

23. 

27.8142-4-307 

11. 

2.268-4-27 

24. 

425.92-4-605 

12. 

2.867-4-47 

25. 

901.57-4-97 

13. 

36.54-4-42 

26. 

.2322-4-86 

14. 

.666-4-74 

27. 

34.356-4-409 

15. 

6.675-4-89 

28. 

45.76-4-650 

DIVISION  103 

Making  the  divisor  an  integer. 
1      fi  25  _i_  1  25  =  5  Study  of  Problems 

2.  62.5  -s-  12.5  =  5  1-    What  is  the  first  quotient?  the  secoml  ? 

3.  625.-5- 125.  =  5        the  third? 

2.    What  was  done  to  the  first   problem  to 
make  the  second?  to  the  second  to  make  the  third? 

3.  How  is  a  decimal  affected  by  moving  the  decimal  point  one  place 
to  the  right  ?  two  places  ? 

4.  How  did  moving  the  decimal  point  to  the  right  the  same  number  of 
places  in  both  dividend  and  divisor  of  each  problem  affect  the  quotient? 

Multiplying  both  dividend  and  divisor  by  the  same  number 
does  not  change  the  quotient. 

Written  Work 

Since  multiplying  both  dividend  and  divisor  by  the  same 
number  does  not  change  the  value  of  the  quotient,  make  the 
divisor  an  integer  before  beginning  to  divide. 

1.  6.48  -4-  .4  =  64.8  ■*■  4.  1-   Make  the  divisor  an  integer  by 

±\a\  a  moving  the  decimal  point  one  place 

^  '    '  to  the   right  in   both    dividend  and 

divisor. 

2.  Show  that  this  does  not  affect  the  quotient. 

3.  Solve,  placing  the  decimal  point  directly  below  the  point  in  the 
dividend,  before  beginning  to  divide. 

2.     57.6  -r-  .024  =  57600  -5-  24.  1.    Make  the  divisor  an  in- 

2400.  teger  by  moving  the  decimal 

24^57600  point  three  places  to  the  right 

'  ,'  in  both  dividend  and  divisor. 

4o 
— —  2.   Solve,  placing  the   deci- 

°"  mal  point  directly  above  the 

96  point  in  the  dividend,  before 

000  beginning  to  divide. 

Divide   as   in  integers,  placing  the  decimal   point  directly 

above  or  below  the  decimal  point  in  the  dividend,  before  begin- 
ning to  divide. 


104  DECIMAL   FRACTIONS 

The  use  of  the  caret  in  division  of  decimals. 

Many  teachers  prefer  to  mark  off  by  a  caret  as  many  deci- 
mal places  from  the  right  of  the  decimal  point  in  the  dividend 
as  there  are  decimal  places  in  the  divisor,  and  divide  as  in 
integers,  placing  the  decimal  point  directly  below  or  above 
the  caret  in  the  dividend.     Thus, 

. 8)5.68  =  .8)5.6A8 
7.1 

It  is  evident  in  the  above  problem  that  if  both  the  divi- 
dend and  divisor  were  changed  so  as  to  make  the  divisor  a 
whole  number,  the  decimal  point  in  the  dividend  would  be 
in  the  place  occupied  by  the  caret,  and  that  the  decimal  point 
would  be  placed  in  the  quotient  immediately  after  the  num- 
bers to  the  left  of  the  caret  had  been  used  in  the  process  of 
division. 

The  use  of  the  caret  determines  the  position  of  the  decimal 
point  in  the  quotient,  and  at  the  same  time  retains  the  iden- 
tity of  the  problem.     Thus, 

l.    Divide  96.8  by  .004.         2.    Divide  1.2864  by  .032. 

.004)96. 800A  .032)1.286,4(40.2 

24  200.  1  28 

64 
64 

Mark  off  by  a  caret  the  same  number  of  decimal  places  from 
the  right  of  the  decimal  point  hi  the  dividend  as  there  are 
decimal  places  in  the  divisor.  Divide  as  in  integers,  placing 
the  decimal  point  in  the  quotient  immediately  after  all  the 
numbers  to  the  left  of  the  caret  have  been  used  in  the  process 
of  division. 


DIVISION 

Find  quotients  : 

3. 

4.05 -.27 

19. 

1000  -  .001 

4. 

.252-=- .14 

20. 

.2375 -j- .095 

5. 

8.398 -h  3.8 

21. 

177.8028-72.87 

6. 

2.173 -s- 1.06 

22. 

145.908  -=- 1.26 

7. 

144 -.12 

23. 

.0656  -=-.004 

8. 

.144-12 

24. 

.1701-63 

9. 

31. 36  -.056 

25. 

85. 75  -=-  .0049 

10. 

.41912 -.338 

26. 

.025641 -.7.77 

11. 

3. 125 -.25 

27. 

.0022-200 

12. 

.3105-15 

28. 

222 -.002 

13. 

.5 -.625 

.025 -=-.00025 

14. 

6.705-^.009 

30. 

.0003-1.5 

15. 

139.195  -*- 14.35 

31. 

$1. 05-1.005 

16. 

46.5 -.1875 

32. 

.685-5-500 

17. 

.00522 -.29 

33. 

.01058-5-46 

18. 

.001705.-5-.  31 

34. 

125.625-5-1.005 

105 


The  division  is  frequently  not  exact.  In  such  cases  the  sign  + 
may  be  placed  after  the  decimal  to  show  that  the  division  is  not  com- 
plete; thus,  1-7  =  .142  + 

Find  the  sum  of  the  quotients  : 


35. 

36. 

37. 

1-  .1  = 

3- 

-  .03  = 

.18-=-  72  = 

.1-  10  = 

30- 

-  .3  = 

.04-=-  50  = 

.25-5-  50  = 

6- 

=-.006  = 

2 -.025  = 

2.5  -5-  .5  = 

16- 

-  .04  = 

20 -.002  = 

25-4-2.5  = 

60- 

-  300  = 

200-12.5  = 

.15-=-.  15  = 

.6-: 

-  30  = 

64 -.016  = 

1.5  h-  15  = 

.66- 

-  1.1  = 

64-  160  = 

.15-5-2.5  = 

.9- 

-.009  = 

.4h-  400  = 

106  DECIMAL   FRACTIONS 

38.  Divide  $.10  by  1100. 

39.  If  a  stone  cutter  earns  $3.75  a  day,  how  many  days 
will  it  take  him  to  earn  $311.25  ? 

40.  If  4275  acres  of  land  cost  $1731.375,  what  is  the 
price  per  acre  ? 

41.  At  $.  22  a  dozen,  how  many  dozen  eggs  can  be  bought 
for  $19.47? 

42.  If  16  stoves  are  sold  for  $292,  what  is  the  average 
price  per  stove  ? 

43.  Divide  $.18  by  $20. 

44.  If  the  wheel  of  a  bicycle  is  9.25  feet  around,  how 
many  times  does  it  turn  in  going  a  mile  ? 

45.  The  product  of  two  numbers  is  .9375.  One  of  them 
is  .75.     What  is  the  other  ? 

46.  There  are  30  \  square  yards  in  one  square  rod.  How 
many  square  rods  are  there  in  a  plot  containing  559.625 
square  yards  ? 

47.  A  merchant,  in  closing  out  his  stock  of  goods,  sold 
.37^  of  the  stock  the  first  month,  .35  the  second  month,  and 
the  remainder,  $5500  worth,  the  third  month.  What  was 
the  value  of  his  stock  of  goods  ? 

Changing  a  common  fraction  to  a  decimal. 

Written  Work 

Since    A  =  4  -=-  5,    to    change    a    fraction    to    a    decimal, 
consider  it  a  problem  in  division  of  decimals.     Thus,  -|  = 
4-3-5  =  5)4.0 
0.8 

Change  to  decimals  and  test : 

■■■•8  *'      12  5<     ff  7-     T6  9'      16 

2-3  4-5-  fill  «19  ir»17 

*'     J  *'      16  **      25  8       32  10-     2~5 


REVIEW    OF    DECIMALS  1Q7 


When  the  division  does  not  terminate,  the  quotient  may  he 
shown  as  a  complex  decimal.      Thus,  ^  =  7)3.000    or  as  an 

0.4281 


7)3  000  u.-*z82- 

incomplete  decimal,     J  ' 

0.428 


11. 

t*t 

12. 

9 
31 

13. 

45 
7  3 

14. 

29 
53 

13.  .45^  +  0.42^5  4-   8.7£      +  .95^  = 

14.  86.55      +9.05^4-   9.87|    +.00-|   =■ 


15.  .875     +  0.75      +   7.7        +  .  41  g   =- 

16.  +  +  + 


1 
6(J 


Change  to  complex  or  incomplete  decimals  of  not  more 
than  four  places  : 

15.  lj  19.    |f  23. 

16.  A  »■     !i  24.     & 

17.  V-  21.     £  25.     2  7 

18.  ff  22.     £-  26.      is 


REVIEW  OF  DECIMALS 

1.  Addf,  .045,  .12|,  18f,  .675. 

2.  Subtract  f  from  .5  of  3|. 

3.  Multiply  (36.7  -  4|)  by  6.7. 

4.  Subtract  6|  from  11.065. 

5.  Take  .0031  from  6. 

6.  Divide  .047f  by  2.3|. 

Add  as  indicated  and  test  : 

7.  8.  9.  10. 

11.  8.375     4-    .025    +   6.24f    +.87]    =— 

12.  .05f     +6.041    +98.005| +.05|   =- 


108 


DECIMAL   FRACTIONS 


BUSINESS  APPLICATIONS  OF  DECIMALS 

In  all  business  transactions  three  things  must  be  considered  : 

(1)  The  quantity  of  the  commodity  bought  or  sold. 

(2)  The  price  per  unit  at  which  it  is  bought  or  sold. 

(3)  The  total  amount  paid  or  received  for  the  commodity. 
Quantity  is  measured  by  standard   units   established    by 

custom  or  law  ;  thus,  the  pound  is  a  unit  of  weight ;  the  foot 
or  the  yard,  a  unit  of  length ;  and  the  gallon  or  the  barrel,  a 
unit  of  liquid  measurement. 

The  price  per  unit  is  the  amount  of  money  paid  or  re- 
ceived for  a  standard  unit  of  the  commodity  ;  thus,  when 
butter  is  sold  at  25  ^  per  pound,  the  standard  unit  is  the 
pound  and  the  price  is  25  cents. 

1.  What  standard  is  used  in  measuring  grain  ?  butter  ? 
eggs  ?  milk  ?  cloth '?  hay  ?  oil  ? 

2.  What  unit  is  used  in  measuring  values  in  money  ? 
How  many  cents  are  there  in  $1  ?  in  $%  ?  •$ \  ?  $>§  ?  50  ^  is 
what  part  of  $1  ?   20  f  is  what  part  of  ffl  ?  25  i  ?  10  ^  ?  5 1  ? 


Parts  of  $1  that  Should  be  Known 


U    =T*o<>f$l 

25^   =iof$l. 

2^   -^    of$l 

33^  =  £of$l 

2^  =  TV   of$l 

37.^  =  fof$l 

4^   =£,   of$l 

40?   =fof$l 

5^  =^    of  $1 

50^   =,Vof$l 

6^  =  TV   of$l 

62^  =  |  of  $1 

Sh?  =  T\   of$l 

66|^  =  |of$l 

10^   =1V    of$l 

75^   =fof$l 

12^=  |     of$l 

80^   =iof$l 

16^=i    of$l 

83^  =  £<>f$l 

20^   =  i    of  $1 

87^  =  |of$l. 

BUSINESS   APPLICATIONS   OF    DECIMALS  L09 

Finding  the  total  cost  when  the  quantity  purchased  is  given 
and  the  price  of  a  unit  is  an  even  part  of  $1. 

Written  Work 

Business  computations  may  be  shortened  by  knowing  the 
relation  that  the  price  of  a  unit  bears  to  $1  or  to  $100. 

1.  How  much  will  44  bushels  of  potatoes  cost  at  $.25  per 

bushel  ? 

Decimal  Method  Short  Method 

$  .25  =  price  ±)$U 

44,  no.  of  bushels  "$TT" 

1  qq  At  $  1  each,  44  bu.  would  cost  $44. 

$iT00  =  total  cost  Atneach,theycostiof«44,or«ll. 

Find  the  cost  of  the  quantity  at  $1.     Divide  this  by  the 
quantity  that  can  be  purchased  for  $  1. 

Find  cost  of  : 

2.  60  bu.  apples  at  33^  per  bushel. 

3.  25  lb.  butter  at  25^  per  pound. 

4.  960  yd.  calico  at  6^  per  yard. 

5.  50  lb.  lard  at  121^  per  pound. 

6.  80  lb.  rice  at  12 1 -fl  per  pound. 

7.  120  yd.  ribbon  at  371**  per  yard. 

8.  500  books  at  40^  each. 

9.  1200  doz.  eggs  at  25^  per  dozen. 

10.  600  bu.  oats  at  33^  per  bushel. 

11.  1600  bu.  coal  at  6|^  per  bushel. 

12.  86  qt.  cherries  at  6|  ^  per  quart. 

13.  2500  bu.  corn  at  40^  per  bushel. 

14.  160  lb.  beef  at  10  4  per  pound. 


110  DECIMAL  FRACTIONS 

15.  A  merchant  buys 

240  lb.  coffee  at  12|  t  per  pound, 
300  lamp  chimneys  at  8^  each, 
6000  qt.  milk  at  41^  per  quart, 
560  bu.  potatoes  at  50^  per  bushel. 
Find  total  cost. 

16.  A  farmer  sells 

1260  heads  of  cabbage  at  b$  per  head, 
250  bu.  potatoes  at  50^  per  bushel, 
2240  lb.  beans  at  6|  $  per  pound, 
600  qt.  cherries  at  8^  per  quart, 
1200  qt.  strawberries  at  12|^  per  quart. 
Find  total  receipts. 

17.  A  milk  dealer  bought 

300  bu.  corn  at  50  ^  per  bushel, 

6000  lb.  bran  at  \$  per  pound, 

6000  lb.  hay  at  f>l  per  hundred  pounds. 

He  sold  4000  gal.  milk  at  6\  tf  per  quart.      How  much  did 
he  make  ? 

Finding  the  quantity  purchased  when  the  total  cost  is  given 
and  the  price  of  a  unit  is  an  even  part  of  $1. 

Written  Work 

1.    How  many  yards  of  calico,  at  Q\$  per  yard,  can  be 
purchased  for  $100? 

Decimal  Method  Short  Method 

100  x  16  yd.  =  1600  yd. 
1600.  since  6\f  =  $  fL,  $  1  pays  for  16  yd.; 

$.0625)!$100.0000A  and  $100  pays  for  100  x  16  yd.,  or 

1600  yd. 

Multiply  the  quantity  purchased  for  $1  by  a  number  equal 
to  the  number  of  dollars  invested. 


BUSINESS   APPLICATIONS   OF    DECIMALS  111 

Find  the  quantity  of  each  article  if  a  grocer  invested 

2.  $1G0  in  sugar  at  Q\  f  per  pound. 

3.  $120  in  sugar  at  4^  per  pound. 

4.  $6.00  in  rice  at  10  ^  per  pound. 

5.  $100  in  cloth  at  50^  per  yard. 

6.  $13.00  in  gingham  at  5^  per  yard. 

7.  $3.00  in  cheese  cloth  at  2^  per  yard. 

8.  $  800  in  milk  at  G\  i  per  quart. 

9.  $  100  in  meat  at  12|  t  per  pound. 

10.  $4.00  in  collars  at  12|  ^  each. 

11.  $1.00  in  bananas  at  20  ^  per  dozen  (find  number  of 
bananas). 

12.  A  hotel  keeper  purchased 

$100  worth  of  sugar  at  G\  ^  per  pound, 
$250  worth  of  potatoes  at  33£  ^  per  bushel, 
$60  worth  of  soap  at  2\  ^a  cake. 

Find  number  of  pounds,  bushels,  and  cakes  purehased. 

13.  A  farmer  sold  to  a  merchant 

10  bu.  apples  at  40  ^  per  bushel, 
20  qt.  beans  at  10  $  per  quart, 
16  bu.  potatoes  at  75  ^  per  bushel. 

He  invested  |  of  the  proceeds  in  cloth  at  25  9  per  yard 
and  the  balance  in  coffee  at  12*  ^  per  pound.  How  much 
of  each  did  he  purchase? 

14.  A  grocer  bought  coffee  at  12|  ^  a  pound,  and  sold  it 
for  $39,  thereby  gaining  $G.50.  How  many  pounds  did  he 
buy  ? 


SIMPLE   ACCOUNTS   FOR   BOYS   AND   GIRLS 


An  account  is  a  statement  of  the  receipts  and  disburse- 
ments of  any  person. 

There  are  two  sides  to  an  account :  the  first,  or  debit  side, 
on  which  are  entered  all  receipts;  the  second,  or  credit  side, 
on  which  are  entered  all  disbursements,  or  amounts  paid  out. 

Dr.  indicates  the  debit  side  of  an  account ;  Cr.  indicates  the 
credit  side. 

The  balance  is  the  difference  between  the  debit  and  credit 
sides. 

September  1,  1906 


Cash  on  hand 

Dr. 

Cr. 

Sept.  1 

$12 

10 

Sept.  1 

Note-book,  $.15;  pencil,  if .05 

$ 

20 

Sept.  4 

Arithmetic 

50 

Sept.  5 

Geography 

1 

00 

Sept.  7 

Copy-book,  $.10;  ink  and  pens,  $.08 

18 

Sept.  15 

History 

1 

00 

Sept.  17 

Worked  one  day 

1 

00 

Sept.  25 

Car  fare 

50 

Sept.  29 

Tools 

1 

60 

Sept.  30 

Balance,  Cash  on  hand 

A 

$13 

8 

12 

10 

$13 

10 

Continue  the  balance  of  each  month  through  the  following 
months  to  September,  1907. 

Note  to  Parents.  —  Children  should  be  encouraged  to  keep  their 
own  personal  accounts. 

112 


SIMPLE   ACCOUNTS   FOR    BOYS   AND   GIRLS  113 

1.  October.  Oct.  3,  Bought  1  pair  of  shoes,  $2.50.  1 
hat,  $1.50.  Oct. 8,  Repairs  to  bicycle,  $.75.  Oct.  15,  Earned 
$1.50.  Oct.  17,  Worked  for  Mr.  Black  and  received  $.15. 
Oct.  25,  Saturday  outing,  $.60. 

2.  November.  Nov.  5,  Bought  a  sled,  $.95.  Nov.  9, 
Bought  a  cap,  $.75.  Nov.  15,  Shoveled  snow  off  Mrs. 
Graham's  walk,  $.30.  Nov.  17,  Sawed  kindling  wood  for 
Mr.  Goff,  $.50.  Nov.  26,  Bought  a  knife,  $.25.  Nov.  30, 
Ran  errands,  $.35. 

3.  December.  Dec.  3,  Bought  1  pair  of  skates,  $.75. 
Dec.  10,  Received  from  Mr.  Black  for  work  in  store,  $1.00. 
Dec.  17,  Expense  for  school  supplies,  $.17.  Dec.  21,  Received 
from  Mrs.  Williams  for  carrying  in  load  of  coal,  $.30. 
Dec.  22,  Bought  Christmas  presents,  $3.75.  Dec.  25,  Christ- 
mas gift  from  Uncle  James,  $1.00.  Dec.  29,  Expense  for 
having  skates  sharpened,  $.10. 

4.  January,  1907.  Jan.  5,  Received  from  Mrs.  Jones  for 
fixing  doorbell,  $.15.  Jan.  8,  Bought  1  pair  mittens,  $.50. 
Jan.  15,  Delivered  bills  around  town  for  Mr.  Black,  $.50. 
Jan.  25,  Bought  necktie,  $.25.  Jan.  30,  Bought  "  History 
of  French  Revolution,"  $.75. 

5.  February.  Feb.  6,  Worked  on  Saturday  for  Mr.  Black, 
$.75.  Feb.  11,  Shoveled  snow  from  sidewalk  for  Mr.  Hart, 
$.25.  Feb.  16,  Ran  errands,  $.40.  Feb.  20,  Helped  unload 
car  of  feed,  $1.00.  Feb.  26,  Copied  2  leases  for  Mr.  Irwin, 
$.75.     Feb.  28,  Bought  pair  of  gloves,  $1.25. 

6.  March.  March  1,  Cleaned  yard  for  Mrs.  Williams, 
$.50.  March  6,  Bought  2  pairs  of  socks,  $.30.  March  11, 
Bought  new  umbrella  for  mother,  $1.75.  March  15,  Repaired 
fence  for  Mr.  Jones,  $.25.  March  27,  Car  fare,  $.30.  March 
30,  Sold  my  old  bicycle  fur  $5.00. 

HAM.     COMPL.     ARITH.     -8 


114  SIMPLE  ACCOUNTS  FOR  BOYS  AND  GIRLS 

7.  April.  Apr.  1,  Burned  paper  and  refuse  for  Mr. 
Hart,  $.25.  Apr.  8,  Made  garden  for  Mrs.  Black,  $.50. 
Apr.  10,  Whitewashed  cellar  for  Mrs.  Goff,  $.35.  Apr.  15, 
Wheeled  load  of  coal  for  Mr.  Brown,  $.35.  Apr.  25,  Bought 
4  collars  and  2  pairs  of  cuffs,  $.90.  Apr.  30,  Bought  neck- 
tie, $.25. 

8.  May.  May  3,  Bought  straw  hat,  $1.00.  May  7, 
Mowed  lawn  for  Mrs.  Jones,  $.25.  May  13,  Repaired 
Mr.  Brown's  sidewalk,  $.40;  May  30,  Bought  baseball,  $.50. 
May  31,  Received  a  reward  of  $5.00  for  finding  a  pocket- 
book  containing  $50,  which  I  returned  to  owner. 

9.  June.     June  1,  Made   $.20  selling   papers.     June  6,  t 
Worked  a  day  for  Mr.    Black,  $.75.     June  10,    Delivered 
package,  $.25.     June  17,  Bought  ball  bat,  $.50.    June  20, 
Wheeled  a  trunk  for  Mr.  Hart,  $.25.    June  29,  Bought  1  pair 
of  baseball  shoes,  $1.00. 

10.  July.  July  4,  Fireworks,  $.50.  July  6,  Received 
from  Mr.  Black  salary  for  week,  $5.00.  July  12,  Bought 
2  shirts,  $1.50.  July  13,  Received  week's  salary,  $5.00. 
July  15,  Bought  outing  suit,  $6.50.  J^ily  20,  Received  my 
salary,  $5.00.  July  25,  Expense  for  small  articles,  $.95. 
July  27,  Received  my  week's  salary,  $5.00.  July  30,  Re- 
ceived for  overtime,  for  month,  $7.50. 

11.  August.  Aug.  3,  Salary,  $5.00.  Aug.  8,  Bought  1 
pair  of  tan  shoes,  $2.50.  Aug.  10,  Received  salary,  $5.00. 
Aug.  15,  Bought  fishing  tackle,  etc.,  $3.75.  Aug.  17,  Re- 
ceived week's  salary,  $5.00.  Aug.  31,  Expenses  for  2 
weeks'  vacation,  $15.75. 

Sept.  1,  Balance,  Cash  on  hand, . 

Make  out  a  statement  at  close  of  year,  showing  total 
receipts  and  disbursements,  and  proving  final  balance. 


DENOMINATE   NUMBERS 

1.  Write  from  memory  the  following  tables : 

Liquid    Measures,    Dry    Measures,    Avoirdupois    Weight, 
Time  Measures,  and  Measures  of  Length  or  Distance. 

2.  1  yr.  = mo.  = da.  = hr.  = niin.  = 


sec. 


3.  1  mi.  = rd.  = yd.  = ft.  = in. 

4.  1  T.  = cwt.  = lb.  = oz. 

5.  1  bu.  = pk.  = qt. 

6.  1  gal.  = qt.  = pt. 

The  standard  or  principal  units  of  measure  are  as  follows  : 
Liquid  —  gallon.  Length  or  distance  —  yard. 

Dry  —  bushel.  Avoirdupois  —  pound  (i6oz.). 

Time  —  day. 

All  other  measures  are  determined  from  the  above  unit 
measures.  Thus,  the  ton  is  2000  times  1  pound  (16  oz.). 
The  hour  is  ^  of  the  day,  the  period  of  one  revolution  of 
the  earth  on  its  axis. 

A  denominate  number  is  a  concrete  number  whose  unit  is  a 
measure  established  oy  custom  or  law;  as,  10  feet,  in  which 
1  foot  is  the  unit  of  measure,  or  5  pounds,  in  which  1  pound 
is  the  unit  of  measure. 

A  simple  denominate  number  is  a  number  of  one  denomi- 
nation ;   as,  12  rods,  2  ounces,  5  days,  etc. 

A  compound  denominate  number  is  composed  of  two  or 
more  concrete  numbers  that  express  one  quantity;  as,  6 
yards,  2  feet,  4  inches.  Here  yards,  feet,  and  inches  are 
used  to  express  but  one  quantity. 

ll  . 


116 


DENOMINATE   NUMBERS 


REDUCTION   OF    DENOMINATE    NUMBERS 


Change  : 

1.  5^  yd.  to  feet. 

2.  90  in.  to  feet. 

3.  3  yd.  2  ft.  to  feet. 

4.  .5  rd.  to  inches. 

5.  25  ft.  to  yards. 

6.  5.5  hr.  to  minutes. 

7.  .5  mi.  to  rods. 

8.  3.5  gal.  to  pints. 

9.  ^  day  to  minutes. 

10.  .25  bu.  to  quarts. 

11.  |  pk.  to  quarts. 


12.  2  lb.  8  oz.  to  ounces. 

13.  |  cwt.  to  pounds. 

14.  .5  yd.  1  ft.  to  inches. 

15.  .75  mi.  to  rods. 

16.  .25  bu.  to  pints. 

17.  3.5  pk.  to  quarts. 

18.  2  yd.  1.5  ft.  to  inches. 

19.  3.5  min.  to  seconds. 

20.  48  qt.  to  pecks. 

21.  64  pt.  to  bushels. 

22.  64  oz.  to  pounds. 


Written  Work 
l.    Change  3  gal.  3  qt.  1  pt.  to  pints. 


gal. 
3 
4 


qt.   pt. 
3      1 


12 

+  3 


15,  number  of  quarts. 
_2 
30 
+  1 
31,  number  of  pints. 


Observe  that  4  qt.  is  really  the  multi- 
plicand and  3  the  multiplier  in  finding  the 
first  product;  and  that  2  pt.  is  really  the 
multiplicand  and  15  the  multiplier  in  finding 
the  second  product.  In  considering  the  num- 
bers abstractly,  however,  either  factor  may 
be  regarded  as  the  multiplicand  and  the 
arrangement  as  indicated  saves  time. 


REDUCTION 


11' 


2.    Change  .875  gallon  to  pints,  etc. 
.875 


3.500,  number  of  qt. 


1.00,  number  of  pt. 


Siuce  there  are  4  qt.  in  a  gallon,  in  .875  of 
a  gallon  there  are  .875  of  4  qt.,  or  :5..">  qt. 
Since  there  are  2  pt.  in  1  qt.,  in  .5  of  a  quart 
there  is  1  pt.     The  answer  is  3  qt.  1  pt. 


Change 


3.  15  lb.  8  oz.  to  ounces. 

4.  96  ft.  5  in.  to  inches. 

5.  5.5  bu.  to  quarts. 

6.  3.5  pk.  to  pints. 

7.  18  cwt.  25  lb.  to  pounds. 

8.  23  hr.  16  min.  to  minutes. 

9.  8.3  mi.  to  yards. 


.75  yd.  to  inches. 
4|  T.  to  pounds. 


7|  min.  to  seconds. 


10. 

11. 

12. 

13.  6.5  L.  T.  to  pounds. 

14.  63.5  gal.  to  pints. 

15.  £  bu.  to  quarts. 

16.  10|  bu.  to  pecks. 


17.    Change  266  quarts  to  bushels,  etc. 

8)266  There  are  |  as  many  pecks  as  quarts, 

4)33,    110.  of  pk.  +  2  qt.      that  is,  33  pk.  +  2  qt.     There  are  \  as 

8,   no.  of  bu.  -f- 1  pk.      many  bushels  as  pecks,  that  is,  8  bu.  + 

.,      ,      „  1  pk.     Hence,  266  qt.  =  8  bu.  1  pk.  2  qt. 

8  bu.  1  pk.  2  qt. 


Change  to  higher  denominations: 


18.  312  inches. 

19.  6625  yards. 

20.  5281  feet. 

21.  2043  seconds. 

22.  1033  ounces  Av 


28.  43920  in. 

29.  6875  sec. 

30.  56.5  pk. 

31.  684.5  rd. 


23.  347  cwt. 

24.  6095  pounds. 

25.  16857  rods. 

26.  11097  qt.  (Dry). 

27.  952  pt.  (Liquid). 

33.  How  many  gallons  of  milk  will  a  family  consume  in 
75  days,  if  they  use  2  qt.  1  pt.  daily  ? 

34.  How  much  is    received  for   H   bushels  of  chestnuts 
at  8  cents  a  quart  ? 


32.    964|  min. 


118  DENOMINATE   NUMBERS 

35.  How  much  will  15  turkeys,  averaging  14^  lb.  each, 
cost  at  18  cents  a  pound  ? 

36.  If  100  tons  of  coal  are  bought  by  the  long  ton,  at 
12.24  a  ton,  and  sold  by  the  short  ton  at  the  same  price,  how 
much  is  gained  ? 

37.  At  20  cents  an  hour,  how  much  will  a  man  earn  in  26 
days,  working  each  day  from  8  A.M.  to  5  p.m.,  allowing  1 
hour  for  lunch  ? 

38.  If  a  flour  mill  grinds  wheat  at  the  rate  of  1  pint  in  5 
seconds,  in  how  many  hours  and  minutes  will  it  grind  21,600 
bushels  ? 

39.  A  train  goes  104  miles  in  3  hours  and  15  minutes. 
What  is  the  rate  per  hour  ? 

40.  At  2  cents  a  foot  find  the  length  in  miles  and  rods 
of  a  telephone  wire  that  costs  $4672.80. 

41.  If  a  man's  step  averages  2  ft.  6  in.,  how  far  will  he 
travel  in  taking  6600  steps  ? 

Relations  of  denominate  measures. 

1.  |  pk.  is  what  decimal  part  of  a  bushel? 

f  pk.  =  6  qt. 

6  qt.  =  —  bu.  =  .1875  bu. 
4        32 

2.  3  ft.  2  in.  is  what  fractional  part  of  a  rod  ? 

3  ft.  2  in.  =  38  in. 

1  rod  =  198  in. 
3  ft.  2  in.  =  T398?,  or  |f  rd. 

Find  the  fractional  part : 

3.  2|  hr.  is  of  1  day.  6.  1|  pt.  is  of  3  qt. 

4.  71  ft.  is  of  1  rod.  7.  2-|  in.  is  of  10  ft. 

5.  3|  qt.  is  of  1  gallon.  8.  1^  qt.  is  of  2  gal. 


ADDITION'    AND  SUBTRACTION  119 

Find  the  fractional  part : 
9.    15  hundredweight  is  of  1  ton. 

10.  3.5  quarts  is  of  1  bushel. 

11.  280  rods  is  of  1  mile. 

12.  37  pounds  8  ounces  is  of  1  hundredweight. 

13.  440  yards  is  of  1  mile. 

Find  the  decimal  part : 

14.  16  hours  48  minutes  is  of  1  day. 

15.  1  foot  8  inches  is  of  1  rod  2  in. 

16.  180  pounds  is  of  1  ton. 

17.  16  minutes  48  seconds  is  of  1  hour. 

18.  A  machinist  works  10  hr.  per  day  in  summer  and 
8|  hr.  per  day  in  winter.  If  his  wages  in  summer  are  $3.35 
per  day,  at  the  same  rate  find  his  wages  per  day  in  winter. 

ADDITION  AND   SUBTRACTION 

1.  Find  the  sum  of  2  gal.  3  qt.  1  pt.,  4  gal.  1  qt.  1  pt., 
7  gal.  1  pt.,  5  gal.  3  qt. 

gal.        qt.  pt. 

^  3  The  sum  of  the  pints  =  3  pt.  =  1  qt.  and  1  pt. 

4  11  The  sum  of  the  quarts  +  1   qt.  carried  =  8  qt.  = 
7  0          12  gal.  0  qt. 

5  3  0  The  sum  of  the  gallons  +  2  gal.  carried  =  20  gal. 

20    o     r 

Add: 

2.  14  bu.  2  pk.,  5  bu.  6  qt.,  7  qt.  1  pt.,  9  bu.  6  qt. 

3.  5  T.  11  cwt.,  4  T.  15  cwt.  60  lb.,  11  T.  80  lb.,  19  T. 
3  cwt.  64  lb. 

4.  9  yr.  120  da.  8  hr.,  12  yr.  104  da.  17  hr.,  14  da. 

5.  3  wk.  6  da.  15  hr.,  4  wk.  3  da.  9  hr.,  7  wk.  5  da.  14  hr. 


7        3        3 
3        15 

1  Pk. 

6  qt,;  2 

4        16 

Subtract : 

mi.        rd. 

yd.        ft. 

7.    80     120 

0       12 

57     215 

0      14 

120  DENOMINATE   NUMBERS 

6.    From  7  bu.  3  pk.  3  qt.  take  3  bu.  1  pk.  5  qt. 

bu.  pk.        qt. 

1  pk.,  or  8  qt.,  +  3  qt.  =  11  qt.;  11  qt.  -  5  qt. 
6  qt.;  2  pk.  -  1  pk.  =  1  pk.;  7  bu.  -  3  bu.  =  4  bu. 


gal.      qt.      pt. 

8.     23        0        1 

9       3       0 

9.    From  18  hr.  take  9  hr.  16  min.  45  sec. 

Finding  the  difference  in  time  between  two  dates  is  the  most 
practical  application  of  subtraction  of  denominate  numbers. 

10.    Find  the  difference  in  time  between  November  15, 1903, 
and  August  12,  1905. 

Aug.  12, 1005,  is  represented  as  the  12th  day 
yr.^         mo.  da.      of  the  8th  mouth  of  1905,  and  Nov.  15,  1903, 

1905  8  12       as  the  15th  day  of  the  11th  month  of  1903. 

1903        11  15  1  mo.,  or  30  da.,  +  12  da.  =  42 da.;  42  da.  - 

1        8        27      15  (la-  =  27  c,a-'  1  vr-> or  12  mo-'  +  7  mo-  =  19 

mo.;    19   mo.  —  11    mo.  =  8   mo.;    1904   yr.  — 
1903  yr.  =  1  yr. 

Subtract : 

yr.         mo.        da.  yr.         mo.        da. 

li.      1908       7       12  12.    1905       9        1 

1901       9       15  1890       8      15 

13.  How  many  years,  months,  and  days  old  is  each  pupil  in 
the  room? 

14.  General  Robert  E.  Lee  was  born  January  19,  1807,  and 
General  Ulysses  S.  Grant  April  27,  1822.  How  old  was 
each  at  the  close  of  the  Civil  War,  April  9,  1865?  How 
much  older  was  General  Lee  than  General  Grant? 

15.  How  old  is  a  man  to-day  who  was  born  July  3,  1882  ? 


MULTIPLICATION    AND   DIVISION  121 

MULTIPLICATION    AND    DIVISION 

1.  Multiply  3  \vk.  5  da.  9  hr.  by  7. 

wk.         da.  hr. 

o  r  g  7  x  fl  hr.  =  63  hr.  =  2  da- and  15  hr.;  7x5  da. 

=  35  da.;  35  da.  +  2  da.  =  37  da.  =  5  wk.  and  2 

1 da.;  7  x  3  wk.  =  21   wk.;  21  wk.  +  5  wk.  =  26  wk. 

26  2        lo         Hence,  the  answer  is  26  wk.  2  da.  15  hr. 

Multiply  : 

2.  3  gal.  2  qt.  1  pt.  by  3. 

3.  12  bu.  3  pk.  3  qt.  by  6. 

4.  15  T.  5  cwt.  12  oz.  by  10. 

5.  27  wk.  3  da.  14  hr.  by  9. 

6.  23  mi.  124  rd.  11  ft.  4  in.  by  12. 

7.  Divide  54  T.  15  cwt.  72  lb.  by  12. 


54  T.  -r- 12  =  4  T.  and  6  T.  remain- 
ing; 6  T.  =  120  cwt. ;    120  cwt.  + 
io\c\J  Ye  to  15  cwt.  =  135  cwt.;  135  cwt.  h- 12 

=  11  cwt.  and  3  cwt.  remaining ;  6 
cwt.  =  300  lb.;  300  lb.  +  72  lb.  = 
372  lb. ;  372  lb.  -*- 12  =  31  lb. 


T.  cwt.  lb. 


11         31 


Divide  : 

8.  18  wk.  5  da.  21  hr.  by  5. 

9.  188  gal.  1  pt.  by  7. 

10.  88  bu.  3  pk.  4  qt,  by  9. 

11.  61  yr.  11  mo.  18  da.  by  11. 

12.  86  T.  3  cwt.  44  lb.  by  6. 

13.  Find  the  cost  of  19  gross  of  pencils  at  10^  a  dozen. 

14.  A  man  digs  4  rods,  2  yards  of  ditch  in  a  day.     How 
many  rods,  etc.,  can  he  dig  in  6  days  ? 

15.  How  many  packages,  weighing  5  ounces  each,  can  be 
made  from  5  pounds  of  candy  ? 


122  DENOMINATE  NUMBERS 

REVIEW 

1.  If  a  watch  gains  18  seconds  in  a  day,  how  much  too  fast 
will  it  be  in  three  weeks  ? 

2.  How  many  barrels,  each  holding  2  bushels  and  3  pecks, 
will  be  required  to  pack  88  bushels  of  apples  ? 

3.  How  many  bushels  of  potatoes  are  necessary  to  plant 
8|  acres,  allowing  6  bu.  1  pk.  to  the  acre? 

4.  A  merchant  sells  linseed  oil  at  12  ^  a  pint  that  cost  him 
56^  a  gallon.     Find  his  profits  on  45  gallons  3  quarts. 

5.  5  car  loads  of  coal  weigh  :  57,698  lb.,  49,875  lb., 
63,545  lb.,  49,897  lb.,  and  54,273  lb.  Find  the  number  of 
tons,  hundredweight,  and  pounds  in  all. 

6.  4  men  buy  a  plot  of  land  that  has  222  feet  8  inches 
street  frontage.  Allowing  for  an  alley  20  feet  in  width  in  the 
center,  what  is  the  width  of  each  man's  lot  if  they  divide  the 
plot  equally  ? 

7.  A  force  pump  in  a  coal  mine  lifts  76|  gallons  of  water 
to  the  surface  per  minute.  Find  the  number  of  gallons 
pumped  out  in  one  day. 

8.  If  3  pounds  4  ounces  of  coal  are  consumed  in  generat- 
ing power  to  lift  5  gallons  of  water  in  problem  7,  find  the 
number  of  tons  of  coal  consumed  each  day. 

9.  A  Kentucky  farmer  clipped  241^  pounds  of  mohair 
from  70  Angora  goats.  Find  the  average  clip  from  each  goat 
and  its  value  at  $.37*-  per  pound. 

10.  An  automobile  runs  2|  miles  in  5  minutes.  At  that 
rate,  find  the  distance  in  miles,  rods,  and  feet  it  runs  in  1 
hour  35  minutes. 

11.  A  pencil  factory  makes  6|  gross  of  pencils  per  hour. 
Find  the  number  of  dozen  made  in  26  days  of  9^  hours  each. 


PRACTICAL   MEASUREMENTS 

MEASURES    OF   LENGTH 

1.  Measure  the  length  of  your  desk ;  the  length  of  the 
room  ;  the  length  of  the  blackboard  ;  the  height  of  the 
window  from  the  floor. 

2.  In  what  are  these  short  lengths  measured? 
To  the  Teacher.  —  Secure  a  tape  measure  50  feet  long. 

3.  Measure  the  distance  around  the  schoolroom  in  feet 
and  fractions  of  a  foot.  How  many  yards  is  it  around  the 
room  ? 

4.  Measure  the  distance  around  the  school  grounds  in 
rods,  feet,  and  inches. 

5.  Take  16|  ft.  of  the  tape  measure  and  measure  10  rods 
along  the  public  road  or  street. 

6.  320  x  16|  ft,  =  how  many  feet? 
1760  x  3    ft,  =  how  many  feet? 

7.  How  many  feet  equal  a  mile  ?     how  many  yards  ? 

8.  James  walks  1|  miles  to  school  each  day.  How  many 
rods  does  he  walk  in  going  to  and  from  school  ? 

9.  How  many  rods  equal  5280  ft,  ?   |  of  a  mile?    3560  ft.? 

10.  Mary  walks  f  of  a  mile  to  school  each  day.  How 
many  miles  does  she  walk  in  going  to  and  from  school  in 
180  days? 

11.  Henry  walks  .8  of  the  number  of  miles  Mary  walks. 
Find  the  distance  Henry  walks  in  a  term  if  he  attends  160 
days. 

123 


124 


PRACTICAL   MEASURED ENTS 


MEASURES    OF    SURFACE 
Observe  that  the  straight  lines  AB  and    CD  cannot  meet, 
however  far  they  may  be  extended.      Such  lines  are  called 
parallel  lines. 


A 
C- 


-B 
■D 


Lines  that  meet,  making  a  square  corner,  form  a  right 
angle. 

A  figure  that  has  four  straight  sides  and  four  right  angles 
is  called  a  rectangle. 

A  rectangle  having  its  four  sides  equal  is  called  a  square. 

1.  Name  six  different  rectangles  in  the  schoolroom.  Are 
the  opposite  sides  of  a  rectangle  parallel  lines  ? 

2.  How  many  dimensions  has  every  rectangular  surface  ? 
How  does  a  surface  differ  from  a  line  ? 


3  in. 


.c 


1 

V 

f                      \ 

3.  Draw,  on  a  scale  of  £,  a 
rectangle  3  inches  long  and  2 
inches  wide.  Divide  it  by  lines 
into  square  inches.  How  many 
square  inches  are  there  in  the 
first  row  ?  in  the  second  ?  in 
the  rectangle  ?  What  is  the 
unit  of  measure  in  this  surface  ? 

Observe  that  2x3x1  sq.  in.  =  6  sq.  in. 

The  area  of  a  rectangle  is  found  by  multiplying  its  unit  of 
measure  by  the  product  of  its  two  dimensions^  when  expressed  in 
like  units. 

4.  Draw  a  rectangle  2  ft.  by  6  ft.     Divide  it  into  sq.  ft. 

5.  Draw  a  square  a  foot  on  a  side.  Mark  off  the  sides 
into  12  equal  parts  and  connect  them  by  straight  lines.  How 
many  square  inches  equal  a  square  foot? 


MEASURES  OF   SURFACE  125 

6.  Draw  oil  the  blackboard  a  line  4  feet  long.  From  each 
end  draw  lines  in  the  same  direction  3  feet  in  length,  making 
square  corners  with  the  4-foot  line.  Connect  by  a  straight 
line  the  ends  of  the  3-foot  lines. 

7.  Are  the  sides  of  the  figure  straight  ?  Are  the  corners 
equal  in  size?     Find  the  area  of  the  figure. 

8.  What  is  a  right  angle  ?  a  rectangle  ?  (p.  124). 

9.  Show  by  a  diagram  the  number  of  square  feet  in  a 
square  yard. 

10.  Draw  a  diagram  on  a  scale  of  1  inch  to  3  feet  to  rep- 
resent a  rectangle  24  ft.  long  and  18  ft.  wide.     Find  its  area. 

Draw  diagrams  on  scales  suitable  to  the  size  of  your  tablet 
or  slate  and  rind  the  surface  of  each  of  the  following : 

11.  A  rectangle  20  ft.  by  24  ft, 

12.  A  flower  bed  16  ft.  by  8  ft. 

13.  A  floor  16  ft.  long  and  14  ft.  wide. 

14.  A  wall  15  yd.  long  and  5  yd.  high. 

15.  By  actual  measurement  find  the  number  of  square  feet 
in  the  floor,  the  door,  the  blackboard,  and  the  walls  of  the 
schoolroom. 

16.  In  what  denominations  did  we  find  the  lengths  and 
widths  of  the  problems  just  given? 

Land  is  measured  in  acres,  square  rods,  square  feet,  etc. 

17.  Measure  a  square  rod  on  your  playground.  How 
long  is  it  ?  how  wide  ? 

18.  Measure  the  length  and  width  of  your  school  grounds 
in  rods  and  feet. 

19.  Since  16^  feet  equal  1  rod,  how  many  yards  equal  1 
rod  ?     How  many  square  yards  equal  1  square  rod  ? 


126  PRACTICAL   MEASUREMENTS 

20.  Since  161  feet  equal  1  rod,  how  many  square  feet  equal 
1  square  rod? 

21.  A  field  is  70  rods  long  and  40  rods  wide.     How  many- 
square  rods  are  there  in  it?  how  many  acres? 

22.  Memorize  this  table  : 


144  square  inches  (sq 

in.) 

=  1  square  foot  (sq.  ft.) 

9  square  feet 

=  1  square  yard  (sq.  yd.) 

30 \  square  yards 

=  1  square  rod  (sq.  rd.) 

160  square  rods 

=  1  acre  (A.) 

640  acres 

=  1  square  mile  (sq.  mi.) 

1  A.  =  160  sq.  rd.  = 

4840 

sq.  yd.  =  43,560  sq.  ft. 

Change : 

23.  2700  sq.  yd.  to  sq.  ft.  26.  If  A.  to  sq.  rd. 

24.  50  sq.  ft.  to  sq.  in.  27.  800  sq.  yd.  to  sq.  rd. 

25.  1600  sq.  rd.  to  A.  28.  5f  A.  to  sq.  ft. 

29.  A  farm  is  90  rods  long  and  60  rods  wide.  Find  the 
number  of  acres  in  it.     Find  its  cost  at  160  per  acre. 

30.  A  lot  100  ft.  square  has  a  house  36  ft.  by  42  ft. 
located  on  it.  The  remaining  space  is  lawn.  Find  the 
number  of  square  feet  of  lawn.     Draw  diagram. 

31.  A  concrete  sidewalk  in  front  of  the  lot  is  4  ft.  wide. 
Find  its  cost  at  19  ^  per  square  foot. 

32.  Find  the  cost  of  a  flagstone  walk,  135  ft.  long  and  6 
ft.  wide,  at  21  i  per  square  foot. 

33.  City  lots  are  sometimes  sold  by  the  square  foot.  Find 
the  cost  of  a  lot  in  Pittsburg  21  ft.  by  70  ft.  at  $27.50  per 
square  foot. 


MEASURES   OF   SURFACE 


127 


34.  A  farm  160  rods  long  and  12<>  rods  wide  is  sold  in 
two  pieces,  §  of  it  at  160  per  acre,  and  the  remainder  at 
$  50  per  acre.     Find  the  amount  of  the  entire  sale. 

35.  An  Iowa  farmer  owns  a  farm  a  mile  square.  How 
many  acres  has  he  ?     Find  its  value  at  $85  per  acre. 

36.  A  western  wheat  held  100  rods  long  and  80  rods  wide 
yields  880  bushels  of  wheat.    Find  the  average  yield  per  acre. 

37.  City  lots  are  usually  sold  by  the  front  foot.  Find  the 
cost,  at  $20  per  foot  front,  of  a  lot  25  ft.  front  by  120  ft. 
deep.     Find  the  cost  per  square  foot. 

38.  A  four-room  school  building  has  a  slate  blackboard 
24  ft.  by  4  ft.  in  each  room.  Find  the  total  cost  of  the 
blackboard  at  23^  per  square  foot. 

39.  The  area  of  a  field  in  the 
form  of  a  rectangle  is  8  acres. 
If  one  side  is  32  rods,  what  is 
the  other? 

These  diagrams  represent  pieces  of 
land.  The  dimensions  are  given  in 
rods,  and  the  corners  are  all  square. 

40.  Divide  the  first  piece  into 
3  rectangles  and  find  (1)  how 

many  square  rods  there  are  in  each  ;   (2)  the  perimeter  of 
each  ;   (3)  the  area  of  the  entire 
piece  in  acres. 

41.  Divide  the  second  piece 
into  rectangular  lots,  and  find 

(1)  the     perimeter     of     each ; 

(2)  the   area  of  each  ;   (3)  the 
area  of  the  entire  piece. 


20 

6 

14 

4 

6 

5 

4 

7 

25 

7 

5      '° 
13 

5 

a 

9 

7 
12 

5 

3 

6 

7 

128  PRACTfCAL   MEASUREMENTS 


PAINTING  AND  PLASTERING 

Painting,  plastering,  and  kalsomining  are  generally  meas- 
ured by  the  square  yard.  In  some  localities  an  allowance  is 
made  for  doors  and  windows,  but  there  is  no  uniform  rule 
in  practice. 

1.  How  much  will  it  cost  to  paint  a  ceiling  18  ft.  long 
and  15  ft.  wide  at  10/  per  square  yard? 

2.  How  much  will  it  cost  to  kalsomine  a  hall  30  ft.  long, 
9  ft.  wide,  and  15  ft.  high,  at  5/  per  square  yard  ?  (Observe 
that  the  perimeter  of  the  hall  is  78  ft.) 

3.  How  many  square  yards  of  plastering  are  there  in  a 
room  21  ft.  long,  18  ft.  wide,  and  12  ft.  high,  making  no 
allowance  for  openings? 

4.  How  much  will  it  cost,  at  15/  a  square  yard,  to  plaster 
a  room  24  ft,  x  191  ft.  x  15  ft.? 

5.  A  public  hall  is  120  ft.  x  G6  ft.  x  22|  ft.  How  much 
will  it  cost  to  paint  the  walls  and  ceiling  at  10/  per  square 
yard? 

THE  RIGHT  TRIANGLE 

1.  Draw  on  the  blackboard  a  rectangle  12  inches  long  and 
8  inches  wide.  Connect  the  opposite  corners  by  a  straight 
line. 

This  line  is  called  the  diagonal  of  the  rectangle. 

2.  Into  how  many  parts  have  we  divided  the  rectangle? 
Shade  one  of  the  parts  with  chalk.  How  many  angles  are 
there  in  each  part  ?  how  many  right  angles  ? 

A  triangle  is  a  surface  bounded  by  three  straight  lines. 


THE   RIGHT   TRIANGLE 


129 


A  right  triangle  is  a  triangle  having  one 
right  angle. 

The  base  of  a  triangle  is  the  side  on 
which  it   is  assumed   to  stand. 

The  altitude  of  a  triangle  is  the  line 
that  meets  the  base  line  at  a  right  angle. 

To  the  Teacher.  —  As  an  aid  in  drawing  have  each  pupil,  if  possible, 
gei  a  right  triangle  as  here  shown. 


3.  Point  out  the  base  and 
altitude  in  the  triangles  at  the 
right. 

o 


4.    Fold  a  rectangular  piece  of  paper,  as  ABCD,  on  its 
diagonal.      Observe : 

(1)  That  the  rectangle  ABCD  and 
the  triansfle  ABB  have  the  same  base 
and  altitude. 

(2)  That  the  area  of  the  triangle 
is  just  I  the  area  of  the  rectangle. 

Hence,  the  area  is  |  of  4  x  2  x  1  sq.  in.  =  4  sq.  in. 


m 

0 

c 

* 

■■"v. 

n 

InllTTThfc. 

■o 

IhTttk 

c 

»~ 

T-> 

ip  ''M 

ilUlHiit^ 

^ 

A    Base   4  in.  B 


The  area  of  a  right  triangle  eqvals  the  unit  of  measure  mul- 
tiplied by  \  the  product  of  the  base  and  altitude. 

Draw  on  a  scale  suitable  to  your  paper  and  find  the  ana 
of  the  following  right  triangles  in  square  inches : 

5.  Base  10  in.,  altitude  8  in.    7.  Base  25  in.,  altitude  18  in. 

6.  Base  12  in.,  altitude  G  in.    8.  Base  St!  in.,  altitude  21  in. 

9.  Find  the  area  of  a  field  in  the  form  o(  a  right  triangle 
whose  base  is  80  rods  and  altitude  40  rods. 

HAM.     COMPL.     AKITU. 9 


130 


PRACTICAL  MEASUREMENTS 


MEASURES  OF  VOLUME 


1.  How  many  dimensions  has  the  cube  ?     Name  them. 

2.  What  dimensions  has  a  line  ?     What  dimensions  has  a 
surface  ?  a  solid  ? 

3.  Name    the   different   units   of   measure   in  which    the 
length  of   a  line  may  be  expressed. 

m4.    Name        the 
^-=  — : -»      different    units    of 

square  measure  in 
which  surface  may 
be  expressed. 

5.  What  cubic 
unit  have  we  in 
the  first  cube  ? 

6.  If  a  cube  is 
1  foot  on  an  edge, 
what  is  the  cubic 
unit  ? 

7.    Draw  a  square  1  foot  on  a  side.     Show  that  it  contains 
144  square  inches. 


MEASURES  OF  VOLUME 


131 


3  in. 


8.  Observe  that  144  cubes  1  inch  on  an  edge  can  be 
placed  on  a  surface  1  foot  square.  How  many  layers  of  such 
cubes  will  it  take  to  make  a  cube  1  foot  on  an  edge  ? 

9.  How  many  cubic  inches  equal  1  cubic  foot  ? 

10.  How  many  surfaces  has  a  cube  ? 

11.  Show  that  all  the  surfaces  of  an  inch  cube  are  the 
same  in  area ;    of  a  2-inch  cube ;    of  a  9-inch  cube. 

12.  Examine  carefully  the  fig- 
ure.     Observe : 

(1)  That  the  surface  of  the 
face  upon  which  it  rests  con- 
tains 9  square  inches. 

(2)  That  the  first  layer  of 
units  of  volume  contains  9 
cubic  inches. 

(3)  That  the  whole  solid,  if 
6  inches  high,  contains  6x9 
cubic  inches,  or  54  cubic  inches. 

13.  How  many  1-inch  cubes 
are  there  in  the  first  layer  ?  how 
many  in  the  solid  ? 

14.  What  is  the  shape  of  the 

surfaces  of  the  solid?     Is  each  surface  a  rectangle? 

A  rectangular  solid  is  a  solid  whose  surfaces  are  all  rectangles. 

15.  Observe  that  the  number  of  inch  cubes  in  the  solid  is 
equal  to  the  product  of  its  three  dimensions. 

16.  What  is  the  unit  of  measure  in  the  solid  ? 
Observe  that  3  x  3  x  6  x  1  cu.  in.  =  54  cu.  in. 

The  contents,  or  volume,  of  a  rectangular  solid  equals  the 
unit  of  measure  multiplied  by  the  product  of  its  three 
diynensions. 


132 


PRACTICAL   MEASUREMENTS 


To  the  Teacher.  —  Secure  144  1-inch  cubes. 

17.  Build  a  cube  2  inches  on  an  edge. 

18.  Build  a  cube  4  inches  on  an  edge. 

19.  Compare  the  4-inch  cube  with  the  2-inch  cube. 

20.  Give   the  different  units   of  measure  of  surface ;    of 
length ;   of  contents. 

21.  Find  the  contents  of  a  box  3  ft.  long,  2  ft.  wide,  and 
11  ft.  high. 

22.    Observe  the  cube.   What 
is  its  length?  width?  height? 

3ft.  23.    How  many  1-foot  cubes 

does  it  contain  ? 

A  cube  3  ft.  on  an  edge  is 
called  a  cubic  yard. 

3f  24.    Memorize  this  table : 


1728  cubic  inches  (cu.  in.)  =  1  cubic  foot  (cu.  ft.) 
27  cubic  feet  =  1  cubic  yard  (cu.  yd.) 


A  cart  load  of  earth  is  considered  1  cubic  yard. 


PRACTICAL   APPLICATIONS 

Excavations  are  estimated  by  the  cubic  yard. 

l.  Find  the  cost,  at  30^  per  cubic  yard,  of  excavating  a 
cellar  36  ft.  in  length,  24  ft.  in  width,  and  4  ft.  in  depth. 

36  x  24  x  4  x  1  cu.fi.  =  3456  cu.  ft.,  the  contents  of  the  cellar. 
3456  cu.  ft.  ^  27  =  128,  number  of  cu.  yd. 
128  x  $.30  =  S  38.40,  cost  of  excavation. 


PRACTICAL    APPLICATIONS 


133 


This  diagram  shows  the  outline  of  a  cellar  5  ft.  deep.     Its 
dimensions  are  given  in  feet. 


2.    Find     its 
square  feet. 


area    in 


4 

4 

14 
14 

30 

12 
12 

30 

3.  Find  the  length  of 
its  walls. 

4.  What  is  the  cost  of 
excavating  it  at  32  ^  per 
cubic  yard? 

5.  How  much  will  it 
cost  to  cement  the  floor  at 
$  .90  per  square  yard  ? 

6.  If  a  boy  inhales  24 

cubic  inches  of  air  at  a  breath,  how  many  times  must  he 
breathe  to  inhale  1  cubic  foot  ? 

7.  29  pupils  and  their  teacher  occupy  a  schoolroom  30  ft. 
in  length,  24  ft.  in  width,  and  12  ft.  in  height.  What  is  the 
average  number  of  cubic  feet  of  air  for  each  person  ? 

8.  A  city  lot  of  37|  ft.  by  120  ft.  is  to  have  a  layer  of  earth 
1  ft.  thick  over  its  surface.  Find  the  number  of  loads 
needed  and  its  cost  at  25  ^  per  load. 

9.  A  dining  room  is  13  ft.  by  18  ft.  and  has  a  rug  on  it 
9  ft.  by  15  ft.     Find  the  surface  not  covered  by  the  rug. 

10.  If  the  rainfall  on  a  certain  day  was  21  inches,  find 
the  number  of  cubic  inches  that  fell  on  a  lot  25  feet  wide 
and  100  feet  long.     Find  the  number  of  gallons. 

11.  Find  the  cost  of  digging  a  ditch,  60  rods  long,  3£  feet 
wide,  and  6  feet  deep,  at  60  ^  per  cubic  yard. 


134  PRACTICAL    MEASUREMENTS 

12.    Memorize : 


1  gallon  =  231  cu.  in. 
1  bushel  =  2150.42  cu.  in. 
1  bushel  =  1]  cu.  ft.  (nearly) 


13.  Compare  a  3-inch  cube  with  a  4-inch  cube.  If  a 
2-inch  cube  weighs  6  ounces,  how  much  will  a  4-inch  cube 
of  the  same  material  weigh  ? 

14.  A  bin  is  8  ft.  long,  6  ft.  wide,  and  4  ft.  deep.  Esti- 
mate quickly  about  the  number  of  bushels  of  wheat  or  oats 
it  will  hold. 

15.  A  farmer  has  a  tank  12  ft.  long,  8  ft.  wide,  and  6  ft. 
deep.      How  many  gallons  of  water  will  it  hold  ? 

16.  How  much  larger  is  a  farm  80  rods  square  than  a 
farm  60  rods  square  ?  Draw  diagrams  on  a  suitable  scale  to 
represent  this. 

17.  The  base  of  a  rectangular  tank  is  48  sq.  ft.  and  the 
volume  is  192  cu.  ft.     Find  the  height. 

18.  What  is  the  area  of  each  surface  of  a  cube  8  ft.  on  an 
edge  ?  the  entire  surface  ? 

MEASUREMENT  OF  LUMBER 

A    board     1    foot 

\iKy ^?  square    and    1     inch 

c        ,-     v  ^  thick  or  less  is  a  board 


I  in. 


foot. 


.{i   4^- A  board  foot  is  the 

vnit     in      measuring 


N         lumber. 


l.    Draw  on  the  blackboard  a  figure  to  represent  a  board 
4  feet  long,  1  fout  wide,  and  1  inch  thick. 


MEASUREMENTS   01    LUMBEB 


! 


4ft. 


2.  Show  that  this  board  contains  4  hoard  feet. 

3.  How  many  board  feet  are  there  in  a  sill  4  ft.  long, 
1  ft.  wide,  and  4  in.  thick? 

Observe  : 

(1 )  That  the  sill  is        rft; 
equal  to  4  boards  1  ft. 
long,  1  ft.   wide,  and 
1  in.  thick. 

( -1  >  That  each  board   contains   4  hoard  fe< 

Hence,  the  -ill  contains  1x4x1  board  foot  =  16  board  feet. 

27//?  number  of  board  feet  in  a  piece  of  lumber  equals  the 
number  of  hoard  feet  in  one  surf 'ace  multiplied  by  the  number 
of  inches  in  thickness. 

Find  the  number  of  board  feel  in  the  following: 

4.  A  plank  12  ft.  long,  12  in.  wide,  and  2  in.  thick. 

5.  A  board  12  ft.  long,  9  in.  wide,  and  1  in.  thick. 

6.  A  plank  15  ft.  long,  12  in.  wide,  and  3  in.  thick. 

7.  A  plank  16  ft.  long,  18  in.  wide,  and  2  in.  thick. 

8.  A  sill  20  ft.  long,  LO  in.  wide,  and  6  in.  thick. 

9.  A  .-.ill  30  ft.  long  and  12  in.  squar< 

Buying  and  selling  lumber. 

Lumber  is  usually  .sold  at  so  much  per  1000  (M.)  board  feet. 

Find  the  cost  of : 

1.  5000  ft.  poplar  at  8  40  per  M. 

2.  500  ft.  hemlock  at  3  24  per  M. 

3.  10,850  ft  Georgia  pine  at  8  24  per  M. 

4.  8000  ft.  white  pine  at  $50  per  M. 

Small  bills  of  lumber  are  usually  estimated  al  90  much  per 

board   foot. 


136 


PRACTICAL   MEASUREMENTS 


5.  Show  that  lumber  at  $  40  per  M.  =  $.04  per  board  foot; 
at  $27  per  M.  =  $.027  per  board  foot. 

6.  Make  out  a  receipted  bill  to  Henry  James  for  the 
following  :  365  ft.  hemlock  at  $  25  per  M.,  780  ft.  white  pine 
at  $40  per  M.,  980  ft.  yellow  pine  at  $29  per  M. 

The  dimensions  10  ft.  by  6  in.  by  10  in.  are  commonly 
written  10'  x  6"  x  10". 

Estimate  the  cost  of  the  following  at  $28  per  M. : 

7.  4  sills  4"  x  8"  x  24'  11.    60  joists  3"  x  8"  x  20' 

8.  6  girders  6"  x  10"  x  16'  12.    90  studding  2"  x  6"  x  16' 

9.  2  posts  6"  x  9"  x  10'        13.    90  planks  2"  x  10"  x  14' 
10.    8  beams  3"  x  8"  x  20'       14.    60  rafters  2"  x  4"  x  24' 

15.  Observe  the  dimen- 
sions of  the  school  build- 
ing. What  is  the  height  of 
the  sides  of  the  building  ? 

16.  Find  the  number  of 
board  feet  of  siding  needed 
for  the  sides  and  the  two 
ends  of  the  same  height  as 
the  sides,  making  no  allow- 
ance for  openings. 

17.  The  triangular  parts 
at  the  top  of  the  house,  in 

front  and  in  back,  are  called  gables.  Each  gable  can  be 
divided  by  a  line  through  the  center  of  its  base  into  two 
right  triangles.  How  many  board  feet  of  siding  are  neces- 
sary for  the  two  gables  ? 

18.  Find  the  cost  of  painting  the  siding  at  10  cents  per 
square  yard. 


S- 28ft.-- 


■-# 


MEASURING    WOOD 


137 


MEASURING  WOOD 


A  pile  of  wood,  of  4-foot  sticks,  8  ft.  in  length  and  4  ft.  in 
height,  is  called  a  cord  of  wood. 

4x4x8x1  cu.  ft.  =  128  cu.  ft.  =  1  cord  of  wood. 

1.  How  man)r  cords  are  there  in  a  pile  of  4-foot  wood, 
160  feet  long  and  4  feet  high  ? 

2.  Two  men  cut  several  piles  of  4-foot  wood  that  measure 
in  all  640  feet  in  length  and  4  feet  in  height.  How  many 
cords  do  they  cut  and  how  much  do  they  receive  for  the  Avork 
at  $5.50  per  cord? 

Wood  is  frequently  cut  for  house  purposes  into  short 
lengths  from  16  inches  to  2  feet.  The  price  of  such  a  cord 
varies  according  to  the  length  of  the  sticks. 

The  number  of  cords  of  short  wood  in  a  pile  is  found  by 
dividing  the  number  of  square  feet  in  one  side  by  32. 

3.  At  a  school  building  there  is  a  pile  of  16-inch  wood  80 
ft.  long  and  4  ft.  high.     Find  its  cost  at  $1.50  per  cord. 

4.  Two  men  cut  4  cords  of  2-foot  wood  each  day  for  16 
days.     Find  the  cost  of  the  cutting  at  70  cents  per  cord. 

5.  One  side  of  a  pile  of  2-foot  wood  contains  400  square 
feet.     Find  the  number  of  cords  it  contains. 


138  PRACTICAL   MEASUREMENTS 

REVIEW  OF  PRACTICAL  MEASUREMENTS 

1.  How  many  tiles  12  in.  square  will  be  required  to  lay 
a  floor  36  ft.  by  15  ft.  ? 

2.  What  is  the  length  of  a  board  walk  that  is  4  ft.  8  in. 
wide  and  contains  1350  sq.  ft.  ? 

3.  How  many  cubic  yards  of  earth  must  be  removed  in 
digging  a  cellar  36  ft.  long,  26  ft.  wide,  and  8  ft.  deep  ? 

4.  Find  the  cost  of  covering  the  floor  of  a  hall  45  ft.  long 
and  30  ft.  wide  with  matting,  a  yard  wide,  at  70  cents  a  yard. 

5.  How  many  times  will  the  wheel  of  an  engine  9  ft.  in 
circumference  turn  in  going  3000  miles  ? 

6.  Find  the  cost  of  30  boards  16  ft.  long,  12  in.  wide, 
and  1  in.  thick,  at  5  ^  a  board  foot. 

7.  At  $.80  a.  bushel  what  is  the  value  of  a  bin  of  wheat 
16  ft.  long,  8  ft.  wide,  and  4  ft.  deep  ? 

8.  What  is  the  number  of  gallons  in  a  tank  12  ft.  long, 
10  ft.  wide,  and  8  ft.  deep  ? 

9.  How  much  will  it  cost  to  cement  the  floor  of  a  cellar 
50  ft.  long  and  28  ft.  wide  at  $1.08  a  square  yard? 

10.  At  7^  a  square  yard,  how  much  will  it  cost  to  paint  the 
four  sides  of  a  building  50  ft.  long,  20  ft.  wide,  and  15  ft. 
high  ? 

11.  My  farm  is  in  the  form  of  a  rectangle,  and  contains  40 
acres.      What  is  its  width,  if  its  length  is  128  rods  ? 

12.  What  will  be  the  cost  of  plastering  the  ceiling  of  a 
room  22  ft.  by  18  ft.  at  11  ^  a  square  yard  ? 

13.  A  rectangular  field  contains  5  acres.  If  its  length  is 
80  rods,  what  is  its  width  ? 


REVIEW   OF    PRACTICAL   MEASUREMENTS  139 

14.  How  many  cakes  of  soap  4  in.  by  3  in.  by  2  in. 
can  be  packed  in  a  box  whose  inside  dimensions  are  2  ft., 
3  ft.,  and  4  ft.  ? 

15.  Find  the  cost  of  digging  a  cellar  42  ft.  long,  30  ft. 
wide,  and  6  ft.  3  in.  deep,  at  40  cents  a  cubic  yard. 

16.  How  much  flooring  1  inch  thick  will  be  required  to 
lay  the  first  floor  of  a  house  22  ft.  by  36  ft.,  no  allowance 
being  made  for  waste,  and  how  much  will  it  cost  at  $30 
per  M.  ? 

17.  The  length  of  a  field  is  80  rods,  and  its  width  is  30 
rods.     How  many  acres  are  there  in  the  field  ? 

18.  What  is  the  number  of  bushels  in  a  bin  20  ft.  long, 
16  ft.  wide,  and  8  ft.  deep  ? 

19.  A  tank  9  ft.  square  and  8  ft.  deep  contains  how  many 
gallons  ? 

20.  A  building  lot  100  foot  front  contains  15,000  sq.  ft. 
What  is  its  depth  ? 

21.  A  baseball  ground  160  yd.  by  170  yd.  has  a  tight 
board  fence  around  it  8  ft.  high.  How  much  will  the  paint- 
ing of  the  outside  of  the  fence  cost  at  5|  cents  a  square  yard  ? 

22.  The  area  of  a  right  triangle  is  560  sq.  ft.,  and  its  alti- 
tude is  28  ft.     What  is  the  base  of  the  triangle  ? 

23.  How  much  will  it  cost  to  excavate  a  street  800  ft.  long 
and  50  ft.  wide,  to  a  depth  of  18  in.,  at  36  cents  a  load  ? 

24.  A  plot  of  ground  in  the  form  of  a  square  is  100  ft. 
on  each  side.  A  straight  walk  8  ft.  wide  divides  it  into  2 
equal  parts  —  a  lawn  for  flowers  and  a  garden  for  vege- 
tables. In  the  lawn  there  is  a  flower  bed  5  ft.  by  8  ft. 
Draw  the  plot. 


140  PRACTICAL   MEASUREMENTS 

25.  Find  the  perimeter  of  the  plot ;  of  the  lawn  ;  of  the 
garden  ;  of  the  flower  bed  ;  of  the  walk. 

Find  the  area  in  square  yards  : 

26.  Of  the  plot.  28.    Of  the  flower  bed. 

27.  Of  the  lawn.  29.    Of  the  walk. 

30.  How  much  will  it  cost  to  fence  the  plot  at  $3f  per 
rod  ? 

31.  How  much  will  it  cost  to  pave  the  walk  at  11.55  per 
square  yard  ? 

32.  How  much  will  it  cost  to  spade  the  flower  bed  at  5 
cents  per  square  yard  ? 

33.  How  much  will  it  cost  to  sod  the  lawn,  excluding  the 
flower  bed,  at  $0.25  per  square  yard  ? 

34.  A  board  16  ft.  long  contains  9  sq.  ft.    Find  its  width. 

35.  A  room  is  20  ft.  long,  16  ft.  wide,  and  10  ft.  high. 
How  much  will  it  cost  to  plaster  the  walls  and  ceiling  at  20 
cents  a  square  yard  ? 

36.  How  many  gallons  of  water  are  there  in  a  tank  12  ft. 
long,  8  ft.  wide,  and  6  ft.  deep,  if  it  is  half  full  ? 

37.  Find  the  cost  of  40  boards,  each  14  ft.  long,  18  in. 
wide,  and  1  in.  thick,  at  8  20  per  M. 

38.  A  city  5  miles  long  and  3  miles  wide  is  equal  in  area 
to  how  many  farms  of  160  acres  each  ? 

39.  How  many  sods  16  in.  square  will  be  required  to  turf 
a  lawn  106  ft.  8  in.  long  and  50  ft.  wide  ? 

40.  What  will  be  the  cost  of  painting  the  outside  of  a 
house  48  ft.  long,  30  ft.  wide,  and  20  ft.  high,  at  18  cents  a 
square  yard  ? 


PERCENTAGE 

Per  cent  means  by  the  hundred  or  hundredths.     The  sign 
for  it  is  %  . 

We    may    express  the  per  cent  of  a  number  either  as  a 
common  fraction  or  a  decimal. 

Thus,  6%  =  rfcj  =  -06  ;    6%  of  500  means  ^ of  500,  which  equals  30; 
or,  expressed  decimally,  .06  of  500  =  30. 

2%  of  a  number  mean's  T§ff,  or  .02,  of  the  number. 
25'/o  of  a  number  means  r2^,or  .25, oi  the  number. 

1.  What   term   in    common  fractions  corresponds  to  the 
number  before  the  sign  %  ?  to  the  sign  %  ? 

2.  What  expresses  the  numerator  and  what  indicates  the 
denominator  of  the  fractions  represented  by  the  following  : 


1%?              20%?              40%? 

90%? 

6%?              30%?              75%? 

100  %  ? 

3.    Find  6  %  of  100. 

jfo  of  100  =  6  ;  or  .06  x  100  = 

=  6. 

4.  5%  of  100 

5.  .05  of  100 

6.  T^  of  100 

7.  6  %  of  150 

8.  .06  of  150 

9.  .10  of  100 


10. 

10  %  of  100 

16. 

8%  of  75 

11. 

25  %  of  100 

17. 

.08  of  75 

12. 

.25  of  400 

18. 

i!o  of  75 

13. 

3  %  of  60 

19. 

331  of  300 

14. 

.03  of  60 

20. 

S31 

ioo  "f  300 

15. 

t§o  of  60 

21. 

33$%  of  300 

111 


142  PERCENTAGE 

Changing  per  cents  to  equivalents. 

Since  5%  =  .05  =  T^  =  2V  these  expressions  may  be  called 
equivalents. 

l.    Give  the  fractional  and  decimal  equivalents  for  10  % ; 
6%;  4%;  20%;  25%. 

Read  the  following  equivalents : 
2.^,20%,  .20,1  s    |7±,  87Wf  .3TJ,  I 

3.  1Q0,  12|%,  .12J,  J  6>  ^  80%,  .80,  I 

4.  ^,  40%,  .40,  f  7.  87i  87i%,  ,87i,  1 

8.   Change  the  fractions  -|,  §,  |,  |    to   their   equivalent 
decimals  and  per  cents ;   also  ^,  |,  |,  |. 


i=  5)1.00 

.20,  or  20% 
I  =  2  x  .20  =  .40,  or  40% 
|  =  3  x  .20  =  .60,  or  60% 
|  =  4  x  .20  =  .80,  or  80% 

*.= 

!  = 
5  _ 

j  — 
7  _ 
j  — 

8)1.00 

.12.1,  or 
3  x  .12V  =  . 
5  x  .12*  =  . 
7  x  .12|  =  . 

37£,  or  37*% 
62|,  or  62J% 
87*,  or  87J% 

Change  to  their  equivalent  decimals  and  per 

cents : 

9    l 
v.    2 

13.  f 

17. 

3 

10 

21.    | 

25.    f 

10.    £ 

14.  i 

18. 

a 

22.    | 

26.    f 

11.    § 

15.    f 

19. 

■A 

23.    i 

27.    | 

12.    1 

16-  tV 

20. 

i 

24.    $ 

•    28'     16 

Give  the  products  rapidly: 

29.  2x.33£ 

32.    5x 

.121 

35. 

4x.l2i 

38.  4x.04l 

30.  5x.l6| 

33.    7x 

.12| 

36. 

6x.l2£ 

39.  3x.l6| 

31.  3x.l2i 

34,    3x 

.81 

37. 

2x.l5 

40.  4x.l6| 

PERCENTAGE  143 

Memorize  the  following  table: 


*  =  50% 

i  =  20% 

f  =  83:\% 

rV  =  8i% 

i  =  33);% 

f  =  40% 

1=13*0 

A  =  41|% 

f  =  66f% 

f  =  60% 

t  =  37|% 

xV  =  6i% 

i=25% 

|  =  80% 

1  =  62->  % 

^f  =  5% 

1  =  75% 

*  =  16f% 

|  =  87.V% 

2^  =  4% 

Name  rapidly  the  fractional  equivalents  of  the  following 
per  cents : 

41.  50%                 46.    20%               51.    37|%  56.    90% 

42.  331%                47.    40%                52.    621%  57.    12.1% 

43.  66|%                48.    60%                53.    87 1  %  58.    16f% 

44.  25%                  49.    16%                54.    10%  59. 


45.    75%  50.    83|%  55.    30%  60.    70% 

Write  the  equivalents  of  the  following  in  decimals,  thus 
1%  =  .01;   32%  =  . 32;   |%  =  .00|;   etc. 


61. 

1% 

67. 

1% 

73. 

50% 

79. 

13% 

62. 

32% 

68. 

3% 

74. 

1% 

80. 

131% 

63. 

1% 

69. 

11% 

75. 

6% 

81. 

1% 

64. 

2% 

70. 

\% 

76. 

\°Io 

82. 

100% 

65. 

16£% 

71. 

4% 

77. 

7% 

83. 

12S% 

66. 

« 

72. 

43£% 

78. 

\% 

84. 

127% 

144  PERCENTAGE 

Finding  a  given  per  cent  of  a  number. 

Recite  the  following  thus  :  Look  at  "  66f%,"  think  "§": 


l.  66f  %  of  18. 

12. 

37|%  of  $7200. 

2.   331%  of  90. 

13 

121%  of  $6400. 

3.  50%  of  $500. 

14. 

75%  of  $4800. 

4.   25%  of  $2000. 

15. 

66|%  of  $999. 

5.   75%  of  16  inches. 

16. 

80%  of  60  sheep. 

6.   20%  of  100  yards. 

17. 

60%  of  75  horses. 

7.  40%  of  60  feet. 

18. 

40%  of  90  miles. 

8.   60%  of  40  miles. 

19. 

871%  of  $160. 

9.  80%  of  75  gallons. 

20. 

621%  of  $240. 

10.  16f%  of  $6000. 

21. 

37|%  of  $880. 

11.  831%  f)f  $1200. 

22. 

121%  0f  24. 

Written  Work 

1.    A  man  had  100  cows 
many  did  he  sell? 

25%  =.25 

and  sold  25  %  of  them.     How 

100  cows 

•25                                    As  25%  = 
500                                result  is  25, 
200 

.25  we  multiply  100  by  .25.    The 
the  number  sold. 

25.00  number  sold 
Find  results  decimally: 

2.  50%  of  750  4.   40%  of  8.75  6.   32%  of  1000 

3.  25  %  of  85.5  5.    28  %  of  840  7.    75  %  of  980 
8.    John  earns  $21.60  per  month,  and  spends  75%   for 

clothes.     How  much  do  his  clothes  cost  him  ? 


PERCENTAGE  145 

9.    There  are  780  pupils  in  school,  and  40%  are  males. 
How  many  are  males  ?  ■ 

10.  If    a  man  buys  a    horse    for   $150  and  sells  it  at   a 

profit  of  20  %,  how  much  does  he  gain  ? 

In  each  of  the  preceding  problems  we  have  two  terms,  a  per  cent 
and  a  whole  or  a  mixed  number.  The  per  cent  in  each  problem  is  the 
multiplier,  and  is  called  the  rate.  The  whole  or  the  mixed  number  is  the 
multiplicand,  and  is  called  the  base.     The  product  is  called  the  percentage. 

The  base  is  that  number  of  which  some  per  cent  is  to  be 
taken  ;  as,  5  %  of  $  200  (base}. 

The  rate  is  the  number  of  hundredths  taken ;  as,  5% 
(rate)  of  80  horses ;  that  is,  ^^  of  80  horses. 

The  percentage  of  a  number  is  the  result  obtained  by  tak- 
ing any  per  cent  of  it ;  as  10  %  of  200  acres  is  ^q  of  200 
acres,  or  20  acres  (percentage). 

11.  What  is  75%  of  85.12? 

Multiplier        Multiplicand         Product 
Rate  Base  Percentage 

75%       of      $5.12     =     (        ) 

Decimal  Method  Study  of  Problem 

75  %  =  .75.  What  is  the  base  ?  $5.12.     What  is  the 

$5.12  =  base  rate?  75%- 

-r  To  what  do  the  base  and  rate  correspond 

— - — —  in    simple    multiplication?      Multiplicand 

^"uv  and  multiplier. 

3o84  To  what  does  percentage  correspond  in 

£3.8400  =  percentage  simple  multiplication?     Product. 

How    is   the   product   found    in    simple 

Fractional   Method  multiplication?    Multiplier  y.  multiplicand. 

75  %  =  f  How  is  the  percentage   found?     Rate  X 

|  of  $5.12  =  ¥3.84         base' 

The  percentage  of  a  number  equals  the  product  of  the  base 
by  the  rate. 

HAM.    COMPL.     A  KITH.  —  10 


146  PERCENTAGE 

Find : 

12.  6  %  of  1200.  17.   8  %  of  400. 

13.  33|  %  of  6  months.  18.  7  %  of  400  horses. 

14.  60  %  of  30  days.  19.  3^  %  of  99. 

15.  1  %  of  100  acres.  20.  6  %  of  150  lb. 

16.  5  %  of  100  acres.  21.  1|  %  of  $75. 

22.  80  is  the  base,  25  %  is  the  rate,  find  the  percentage. 

23.  A  house  costs  $2500,  and  the  damage  by  fire  is  8%. 
Find  the  amount  of  the  damage. 

24.  John  owes  his  tailor  $80,  and  pays  37 1  %  of  the  debt. 
How  much  does  he  still  owe  ? 

25.  Mary  spells  90  %  of  80  words  correctly.     How  many 
does  she  miss  ? 

26.  A  boy  buys  apples  at  $1  per  bushel,  and  sells  them  at 
a  profit  of  20%.     How  much  profit  is  that  per  bushel  ? 

27.  G|  %  of  3680  equals  what  number  ? 

28.  A  man  bu}Ts  a  farm  for  $2500,  and  sells  it  for  25  % 
more  than  it  cost  him.    For  how  much  does  he  sell  the  farm  ? 

29.  A  man  earns  $180  per  month,  and  puts  33^  %  of  it  in 
the  savings  bank.     What  is  his  deposit  each  month  ? 

30.  If  37|  %  of  a  man's  farm  is  in  timber,  and  the  total 
area  is  240  acres,  how  much  timber  land  has  he  ? 

31.  A  teacher  who  earned  $1200  a  year  spent  66|  %  of  her 
salary.     How  much  did  she  save  ? 

32.  Mr.    Scott's  horse  is  valued  at  $250  and  Mr.  Hill's 
at  60%  of  this.     What  is  the  value  of  Mr.  Hill's  horse  ? 

33.  The  population  of  a  town  of  9672  inhabitants  increased 
12-i-%  [n  a  vear#     What  was  the  increase  in  population? 


COMMISSION  147 

COMMISSION 

An  agent  is  a  person  who  transacts  business  for  another. 

Commission  is  the  sum  charged  by  an  agent  or  commission 
merchant  for  his  services. 

The  net  proceeds  is  the  sum  left  after  the  commission  and 
other  expenses  have  been  paid. 

l.  A  real  estate  agent  sold  a  house  for  15000,  retaining 
5%  of  this  sum  for  his  services.  How  much  did  he  receive? 
How  much  did  the  owner  receive  ? 

$5000  =  selling  price. 

.05  —  rate  charged  by  the  agent. 


$250.00  =  amount  charged  by  the  agent. 
$5000  -  $250  =  $4750,  amount  received  by  the  owner. 

A  commission  merchant  made  the  following  sales.  Find 
his  commission  for  each  day  at  5  %. 

2.  Monday,  $1800  5.    Thursday,  11400.80 

3.  Tuesday,  $1594  6.    Friday,  $1528 

4.  Wednesday,  $1954  7.    Saturday,  $2370.60 

8.  Find  his  total  commission  for  the  week. 

9.  A  real  estate  agent  sells  a  house  and  lot  for  $6750, 
charging  2%  commission.  Find  his  commission  and  the 
net  proceeds. 

10.  A  traveling  salesman  sold  $50,000  worth  of  goods  in 
a  year  at  a  commission  of  8%.  If  his  expenses  for  the  year 
were  $2200,  how  much  had  he  left? 

11.  An  agent  rents  12  houses  at  $40  per  month.  If  he 
receives  5%  for  collecting  the  rents,  how  much  is  remitted 
to  the  owners  each  month  ? 


148 


COMMERCIAL   DISCOUNT 


COMMERCIAL   DISCOUNT 

Wholesale  merchants  and  manufacturers  usually  publish 
printed  price  lists  of  their  goods.  The  prices  in  these  lists 
are  higher  than  the  wholesale  prices  and  are  subject  to 
deductions  called  trade  discounts  or  commercial  discounts. 

Note.  —  A  discount  is  any  deduction  from  a  fixed  price. 

Sometimes  several  discounts  are  allowed.  The  first  is  a 
discount  from  the  list  price;  the  second,  a  discount  from  the 
remainder,  etc. 

The  net  price  is  the  price  less  all  trade  discounts. 

Find  the  selling  price  of  goods  marked  : 


1. 

$15,  less  20%. 

7. 

$40,  less  60%. 

2. 

$20,  less  40%. 

8. 

$48,  less  25%. 

3. 

$6,  less  50%. 

9. 

$6.80,  less  25%. 

4. 

$25,  less  20%. 

10. 

$4.50,  less  331%. 

5. 

$7.50,  less  20%. 

11. 

$9.60,  less  16§  %. 

6. 

$12.50,  less  40%. 

12. 

$4.80,  less  371%. 

Written   Work 

Find  the  selling  price  of  goods  marked  : 


1.  $168.75,  less  25%. 

2.  $1374,  less  16|%. 

3.  $1872,  less  331%. 

4.  $278.40,  less  371%. 

5.  $3030  less  40%. 
Find  the  cost  of  : 

Discount,  20% 

11.      60  readers  @  $  .40 
150  geographies  @  $  1 
78  grammars  @  $  .60 


6.  $225.65,  less  20%. 

7.  $875.50,  less  30%. 

8.  $278.90,  less  10%. 

9.  $2378.50,  less  4%. 
10.  $6775.20,  less  5%. 

Discount,  4  % 

12.    160  lb.  rice  @  $.06 
300  lb.  sugar  @  $.041 
200  lb.  coffee  @  $.16 


COMMERCIAL    DISCOUNT  149 

13.  Find  the  net  price  of  a  bill  of  goods  for  $  75.40,  trade 
discounts  20%,  10%. 

List  price,  $  75.40 

1  ess  °0  °!  15  08         Observe    that    the    second    discount   is 

,,.  .     ,      — Ql.  .,  ,    reckoned  on  the  first  remainder.     As  there 

tirst  remainder,    00. o'l  .  ,.  ,, 

are  only  two  discounts,  the  second  reinam- 

Less  10  %,  6.03     der  is  the  net  price. 

Net  price,  $51.29 

Find  the  net  price  of  articles  listed  at : 

14.  $100,  less  20%,  10%.       17.    $  10.75,  less  40%,  5%. 

15.  375.50,  less  25  %,  5  %.       18.    $  6.80,  less  25  %,  10  %. 

16.  290.80,  less  40%,  10%.     19.    112.75,  less  331%,  10%. 

Find  the  net  price  of  the  following  bills  of  goods : 

20.  36  dozen  boys'  caps  @  $  6,  discounts  25  %,  20  %. 

21.  50  buggies  @  $  120,  discounts  20%,  15%. 

22.  75  sets  harness  @  $  40,  discounts  30%,  10  %. 

23.  25  grain  drills  @  $  95,  discounts  40  %,  5%. 

24.  12  rubber  hose,  each  50  feet  long  at  15^  per  foot, 
discounts  30%,  15%. 

25.  Mr.  Austin  buys  a  wagon  listed  at  $95,  less  20% . 
15%.     Find  the  amount  paid  for  the  wagon. 

26.  A  merchant  buys  12  stoves  listed  at  $45,  less  40%, 
10  %.  Find  the  net  amount  of  the  bill.  Compare  this  with 
the  net  amount  of  the  bill  with  only  one  discount  of  50  %. 

27.  A  hotel  keeper  buys  675  yards  of  carpet  at  $1.25, 
less  20  %,  5  %.     Find  the  cost  of  the  carpet. 

28.  Compare  the  net  price  of  an  article  listed  at  $500, 
discounts  of  20  %,  10  %,  with  the  net  price  of  a  similar  article 
listed  at  $500,  discounts  of  10  %.  20  %. 


150  COMMERCIAL    DISCOUNT 

Solve  according  to  conditions  : 

29.  The  Packard  Hardware  Co.  bought  for  cash  from 
Jas.  M.  Armstrong  Co.,  Chicago,  111.,  4  doz.  Acme  lawn 
mowers  @  $30  a  dozen,  50  lb.  lawn  seed  @  15^  a  pound,  2^ 
doz.  brushes  @  40^  a  dozen.  Trade  discounts:  20%,  10%. 
Terms:  30  days  net;  2%  cash  in  10  days. 

Cost  of  bill  of  goods  =  ,1128.50. 

■1128.50  less  trade  discount  of  20%  =  1102.80;  $102.80  less  trade  dis- 
count of  10%  =  f92.52,  net  price  of  bill  if  paid  in  30  days.  If  the  bill  is 
paid  within  10  days  from  date  of  purchase,  the  buyer  gets  a  further  dis- 
count of  2%.  This  is  called  a  cash  discount.  $92.52,  less  2%  for  cash 
within  10  days,  =  $90.68. 

30.  Jamison  and  Redmond,  South  Bend,  Ind.,  bought 
for  cash  from  the  Acme  Buggy  Co.,  Cincinnati,  O.,  72 
buggies  @  $105,  50  sets  harness  @  $45,  15  sleighs  @  $60, 
40  robes  @  $20.  Trade  discounts:  30%,  15%.  Terms: 
30  days  net ;  3  %  cash  in  10  days. 

31.  James  Cubbison,  Greenville,  O.,  buys  for  cash  from 
Arbuthnot,  Stevenson  &  Co.,  Pittsburg,  Pa.,  5  doz.  hand- 
kerchiefs @  $3.60;  5  bolts  muslin,  40  yd.  each,  @  8^;  5 
bolts  prints,  42  yd.,  @  7  ^.  Trade  discount :  33^%.  Terms: 
30  days  net ;   2  %  cash  in  10  days. 

32.  S.  H.  Gardner  Co.,  piano  dealers,  Detroit,  Mich., 
order  from  the  Harmonic  Piano  Co.,  Chicago,  111.,  2  Har- 
monic pianos  #266  @  $600,  less  40%,  10%  trade  discount. 
Terms  :  90  days  net ;  10  %  off  10  days.  Find  the  cash  price. 
Find  the  net  price  if  paid  in  30  days. 

Notk.  —  The  sign  #,  when  placed  before  a  number,  is  read  "  number." 

33.  M.  L.  Smith,  tailor,  Brockton,  Mass.,  orders  from 
Bender  &  Co.,  New  York,  importers,  3  pieces  suiting,  22  yd. 
each,  @  $3.15.  Terms:  30  days  net;  2%  off  10  days. 
Find  the  net  amount  of  bill  if  paid  within  10  days. 


INTEREST 

1.  Mr.  Johnston  pays  the  liveryman  $6  for  the  use  of  a 
horse  and  buggy  for  two  days.  What  does  he  get  in  ex- 
change for  the  $6? 

2.  Mr.  Daniels  pays  $6  for  the  right  to  pasture  his  cow 
in  a  field  for  two  months.  What  does  he  get  in  exchange 
for  the  $6? 

3.  Mr.  Watson  pays  $6  for  the  use  of  #100  for  one  year. 
What  does  he  get  in  exchange  for  the  $6  ? 

4.  In  the  first  two  examples  money  is  paid  for  the  use  of 
something  that  is  not  money.  For  what  does  Mr.  Watson 
pay  the  money  in  the  last  example  ? 

Interest  is  money  paid  for  the  use  of  money.  Interest 
corresponds  to  the  percentage  in  percentage. 

5.  How  much  does  Mr.  Watson  pay  for  the  use  of  the 
money?     What  is  the  $6  called  ? 

6.  On  what  is  the  interest  reckoned  ?  The  $100  is  called 
the  principal. 

The  principal  is  the  sum  on  which  the  interest  is  paid. 
The  principal  corresponds  to  the  base  in  percentage. 

The  rate  of  interest  is  a  certain  number  of  hundredths  of 
the  principal  paid  for  the  use  of  the  principal  for  one  year. 

Time  is  always  a  factor  in  interest.  Interest,  then,  is  the 
product  of  three  factors:  principal,  rate,  and  time. 

The  amount  is  the  sum  of  the  principal  and  the  interest, 

151 


152  INTEREST 

Interest  for  Years  and  Months 

1.  What  part  of  a  year  are  6  months  ?  4  months  ?  3 
months  ?    2  months  ?    1   month  ? 

2.  If  the  interest  for  a  year  is  $100,  what  should  it  be  for 
6  months  ?  for  4  months  ?  for  3  months  ?  for  2  months  ?  for 
1  month? 

Written  Work 

1.    What  is  the  interest  on  -1200  for  2|  years  at  6  %  ? 

$200  principal  .  . 

11  1  he  interest  for  1  year  is  .06 

of  the  principal,  or  .$12.    The  in- 


il2.00  interest  for  one  year      terest  for  2\  years  is  2\  x  $12,  or 


21  $30. 


$30.00  interest  for  2|  years 

Multiply  the  'principal  by  the  rate  and  the  product  by  the 
number  of  years. 

The  year  is  usually  considered  as  360  days,  that  is,  12  months  of  30 
days  each. 

Find  the  interest  on  : 

2.  $300  at  5%  for  1  year.     4.    $150  at  6.}  %  for  3  years. 

3.  $800  at  8  %  for  2  years.     5.    $700  at  4|  %  for  4  years. 

Find  the  interest  of  : 

6.  $250  fori  |  years  at  4%.   11.    $500  for  21  years  at  4|  %. 

7.  $75  for  2  years  at  8  %  .  12.  $960  for  9  mo.  at  6  %. 

8.  $100  for  3f  years  at  7%.  13.  $900  for  2f  years  at  7  %. 

9.  $  80  for  41  years  at  5  % .  14.  $654  for  f  year  at  6  % . 
10.  $40  for  21  years  at  6-1  % .  15.  $  220  for  J  year  at  8  % . 


INTEREST   FOR    YEARS,    MONTHS,    AND   DAYS       153 

Find  the  interest  at  6  %  on  : 

16.  $100  for  6  months.  19.  1624  for  120  da. 

17.  $500  for  4  months.  20.  $170  for  8  mo. 

18.  $150  for  2  yr.  2  mo.  21.  $355  for  130  da. 

Interest  for  Years,  Months,  and  Days 

1.  What  part  of  a  month  (30  days)  are  15  days?  12  days  ? 
20  days  ?  3  days  ?  what  part  is  1  day  ? 

2.  If  the  interest  for  1  year  is  $360,  what  is  the  interest 
for  1  month  ?  If  the  interest  for  1  month  is  $  30,  what  is  the 
interest  for  1  day  ?  for  15  days  ?  for  12  days  ? 

Written  Work 

l.    Find  the  amount  of  $  200  at   6  %   interest  for  2  yr. 

7  mo.  12  da. 

Principal  =     $200 

Rate  = .06 

Int.  for  1  yr.  =$12.00 
Int.  for  2  yr.  =  2  x  $12.00,  or  $24.00 

Int.  for  7  mo.  =  T75  of  %  12.00,         or       7.00 

Int.  for 12  da.  =  j$,  or  f,  of  $1.00.  or  .40 

Int.  for  2  yr.  7  mo.  12  da.  =  $31.40 

Principal  =  $200.00 

Amount  for  2  yr.  7  mo.  12  da.  =  $231.40 

Study  of  Problem 

a.  What  is  the  first  step  in  the  work  ?  the  second  step? 

b.  How  do  we  find  the  interest  for  1  month?   for  7  months?    for  12 

days? 

c.  What  new  term  is  introduced  in  interest?  For  what  length  of 
time  is  rate  of  interest  always  considered? 


151  INTEREST 

Find  the  interest  and  amount  of  : 

2.  1300  for  3  yr.  6  mo.  at  6%. 

3.  1 250  for  2  yr.  4  mo.  at  7  %. 

4.  $  160  for  1  yr.  3  mo.  at  5  %. 

5.  $  50  for  1  yr.  8  mo.  at  5  % . 

6.  $  800  for  3  yr.  2  mo.  at  6  %. 

7.  $50.80  for  9  mo.  at  10%. 

8.  $16  for  8  mo.  at  6%. 

9.  $75  for  8  mo.  at  6  %. 

10.  1420  for  10  mo.  at  10  %. 

11.  $40.50  for  1  yr.  1  mo.  at  6  %. 

12.  $  300.40  for  5  mo.  at  7  %. 

13.  $  100  for  7  mo.  at  7  ft, . 

14.  $500  for  11  mo.  at  6  %. 

15.  $1000  for  1  mo.  at  6%. 

16.  $60.(30  for  8  mo.  at  8%. 

Find  the  interest  and  amount  of  : 

17.  $250  at  8  %  for  3  yr.  5  mo.  20  da. 

18.  $75.80  at  5  %  for  4  yr.  1  mo.  16  da. 

19.  $  1500  at  6  %  for  2  yr.  9  mo.  15  da. 

20.  $125.50  at  4  %  for  4  yr.  11  mo.  12  da. 

21.  $  1140  at  5|  %  for  4  yr.  8  mo.  24  da. 

22.  $  912.60  at  5  %  for  2  yr.  10  mo.  11  da. 

23.  $  3209  at  6  %  for  3  yr.  7  mo.  21  da. 

24.  $634.50  at  8  %  for  11  mo.  12  da. 

25.  Henry  Boydson  borrows  $  275  Sept.  1,  1906,  at  6  % 
interest,  and  settles  the  note  Jan.  1,  1908.  Find  the  amount 
of  the  note  at  settlement. 


REVIEW    OF   PERCENTAGE   AND   INTEREST 

1.  A  boy  has  $30  in  a  savings  bank  and  deposits  a  sum 
equal  to  10%  of  it.  What  is  the  total  amount  he  has  in 
bank? 

2.  Mr.  James's  salary  is  $1200  per  year  and  he  saves 
33^%  of  it.     How  much  does  he  spend? 

3.  A  boy  spends  $8  for  an  overcoat  and  37.]  %  of  that 
sum  for  shoes.     How  much  does  he  spend  for  shoes? 

4.  In  a  school  of  45  pupils,  33^  %  of  the  pupils  are  boys. 
What  is  the  number  of  girls  ? 

5.  Find  '2;')%  of  .05;  of  .5;  of  5.5;  of  .25. 

6.  John  earns  $50  during  his  vacation,  and  Margaret 
25%  as  much  as  John.     How  much  does  Margaret  earn? 

7.  A  farmer  sold  a  horse  that  cost  him  $  80  at  a  loss  of 
20%.      Find  the  selling  price. 

8.  What  is  the  interest  on  $150  for  2]  years  at  »!%  ? 

9.  Find  the  interest  on  $100  for  00  days  at  5%. 

10.  My  father  borrows  $75  from  his  neighbor  and  promises 
to  pay  it  in  4  months  at  0%.  Find  the  amount  my  father 
must  pay  at  the  end  of  four  months. 

11.  A  huckster  buys  eggs  at  $.20  per  dozen.  For  how 
much  per  dozen  must  he  sell  them  to  gain  20  %  ? 

12.  If  I  borrow  $50  from  Mr.  James  for  6  months  at  0%, 
how  much  interest  must  I  pay  him? 

155 


156  REVIEW   OF   PERCENTAGE   AND   INTEREST 

13.  A  grocer  sold  flour  last  week  at  $1.20  per  sack  and 
this  week  at  10  %  advance  on  last  week's  selling  price.  Find 
the  price  of  flour  per  sack  this  week. 

14.  A  huckster  buys  150  dozen  eggs  at  $.20  per  dozen  and 
sells  them  to  a  merchant  at  a  gain  of  25  %.  The  merchant 
sells  them  at  a  gain  of  20  %.  How  much  does  the  merchant 
receive  for  the  eggs  ? 

15.  If  I  buy  cloth  at  $1.50  a  yard,  for  how  much  must  I 
sell  it  to  gain  33£  %  '■ 

16.  A  grocer  buys  goods  to  the  amount  of  $1200,  10  %  off 
for  cash.  He  sells  them  for  $1500  cash.  How  much  does 
he  gain  ? 

17.  A  mother  took  two  boys  and  a  girl  to  a  store  to  buy 
clothes.  The  first  boy's  suit  cost  $10  less  10%  for  cash. 
The  second  boy's  suit  cost  66|  %  of  the  cash  price  of  the  first 
boy's  suit.  The  girl's  coat  cost  331%  0f  the  money  paid 
for  both  boys'  suits.  How  much  did  the  mother  pay  for  the 
children's  clothes  ? 

18.  Find  25  %  of  200,  and  divide  the  result  by  .00J. 

19.  A  man  buys  a  house  and  lot  for  $5000.  It  costs 
every  year  $25  for  repairs  and  $50  for  taxes  and  insurance. 
He  rents  the  house  for  8%  of  its  cost.  How  much  has  he 
left  after  paying  expenses  ? 

20.  A  coal  dealer  bought  300  tons  of  coal  for  $600.  The 
freight,  storage,  and  delivery  cost  331  cj0  0f  the  cost  of  the 
coal.  What  was  the  retail  price  per  ton  if  he  sold  it  at  a 
gain  of  12^%  ? 

21.  A  real  estate  agent  purchased  a  house  for  $1250.  For 
how  much  per  month  must  he  rent  the  house  to  make  6  % 
after  paying  each  year  $18  for  taxes  and  insurance  and  $15 
for  repairs  ? 


RECEIPTS   AND   CHECKS 

John  Watson  pays  James  Adams  $ 35.50  for  work  for 
one  month,  and  asks  Mr.  Adams  for  a  receipt.  Write  the 
receipt  to  show  that  the  money  was  paid  by  Mr.  Watson 
and  received  by  Mr.  Adams. 


$ Rochester,  jY.  Y.,  fwyva  /,  1907. 

Eeceifceli  from 

Dollars 

for 


1.  What  must  every  receipt  show? 

2.  Write  the  receipt  your  grocer  would  give  you  in  pay- 
ment of  $18.50  on  account  by  your  father  or  mother. 

3.  Your  school  district  pays  the  National  Book  Company, 
New  York,  $  25.75  for  school  books  on  Sept.  15, 1907.  Make 
out  the  receipt  of  the  National  Book  Company. 

4.  Henry  Smith  received  I  3.65  from  James  Brown  for  3 
months'  water  rent.     Make  out  a  receipt  for  the  amount. 

5.  Ralph  Taylor  pays  II.  W.  Henderson  |5  for  a  month's 
tuition.     Write  the  receipt  Ralph  Taylor  should  receive. 

157 


158  RECEIPTS    AND   CHECKS 

6.  Write  a  receipt  for  $  75  which  Nelson  Page  paid  Edgar 
Poe  for  balance  due  on  a  buggy. 

7.  Make  out  and  receipt  the  bill  for  the  following  articles 
bought  by  James  Thomas  from  Jos.  Home  &  Co.  : 

3  shirts     @$1.75  2  neckties       @     $.75 

6  collars   @        .20  4  pairs  cuffs  @        .20 

8.  Presuming  that  you  are  a  collector  for  the  Gazette- 
Times,  Pittsburg,  Pa.,  make  out  a  receipt  to  a  subscriber  who 
has  paid  you  $  2.60  in  full  of  account. 

A  check  is  an  order  on  a  bank  where  a  person  keeps  a 
deposit,  ordering  the  bank  to  pay  money. 

Stub  Check 


c/t*.  875  J  No.  875 

I  Seattle,  Wash.,  fan.  fO,  1907 

oo  &\>t  gufcon  Rational  Bank  of  Seattle. 

PAY    TO    THE 

i  Order  of- fame*,  lO-avci 


fan.  /O,  '07 

/  &vxiu-4,&v-&K—~~~~~lJoUars 

'  100 

3ov  jCa-6-cyv  i  Z0-.     $.    ?)1oov&. 


1.  Name  the  different  things  stated  in  this  check. 

2.  Observe  that  this  check  is  payable  to  the  order  of  James^ 
Ward.  He  orders  it  paid  by  writing  his  name  across  the 
back  of  it.     This  is  called  indorsing  the  check. 

3.  Write  the  check  your  father  would  give  your  teacher 
in  payment  of  $3.50  for  September  tuition. 

4.  Emil  Smith  borrows  from  Joseph  McLean  $240  to 
attend  school  and  pays  the  same  in  2  yr.  4  mo.  18  da.  at  0%. 
Write  the  amount  of  the  check  that  would  pay  the  note. 


GENERAL  REVIEW 

1.  The  remainder  is  92,568  and  the  minuend  is  202,660. 
Find  the  subtrahend. 

2.  The  dividend  is  364,450  and  the  quotient  is  9850. 
What  is  the  divisor  ? 

3.  Add  3.5,  .035,  45.006,  and  2.06. 

4.  Write  decimally  twenty-five  and  sixty-one  thousandths; 
one  hundred  twenty-five  and  five  tenths  ;  and  three  hundred 
and  two  ten-thousandths. 

5.  What  number  multiplied  by  one  hundred  seventy- 
nine  is  equal  to  848,818  ? 

6.  From  2.0011  take  1.9892. 

7.  Explain  the  difference  between  \°J0  and  \. 

8.  Add  1  2f,  1   ||,  and  4f . 

9.  Find  1%,  -i-,  1%,  fa  £>%,  50%,  and  ^  of  100. 

10.  The  multiplicand  is  1325  and  the  multiplier  is  .0416. 
What  is  the  product  ? 

11.  If   38  dozen  eggs  cost  $11.40,  what  is  the  cost  per 
dozen  ? 

12.  A  building  is  46  ft.  3  in.  wide,  and  twice  as  long  as 
wide.     Find  the  distance  around  the  building. 

13.  From    86   miles  and   3   inches,  take   46  miles  and  8 
inches. 

159 


160  GENERAL  REVIEW 

14.  A  man  and  his  son  together  earn  $72  per  month.  If 
the  man's  earnings  in  6  months  amount  to  $300,  how  much 
are  the  son's  earnings  in  the  same  length  of  time  ? 

15.  A  man  bought  48  head  of  cattle,  at  $36  per  head,  and 
sold  them  at  a  gain  of  25%.  What  was  the  total  amount 
received  for  the  cattle  ? 

16.  Find  the  interest  on  $370.50  for  4  yr.  8  mo.  at  6%. 

17.  Divide  48|  by  21f 

18.  Divide  .65  by  6.5. 

19.  Reduce  187^  rods  to  the  fraction  of  a  mile. 

20.  How  much  will  it  cost  to  ship  a  car  load  of  wheat 
containing  42,000  lb.  from  Fargo,  N.D.,  to  Chicago,  111.,  if 
the  freight  rate  is  $.06  per  bushel  ?     (60  lb.  =  1  bu.) 

21.  A  train  leaves  Chicago  at  8:15  a.m.,  and  arrives  at 
Pittsburg  at  8:20  p.m.  The  distance  is  468  miles.  Find 
the  number  of  miles  per  hour  the  train  travels. 

22.  The  steel  rails  on  the  Bessemer  railroad  weigh  100 
pounds  to  the  yard.  Find  the  number  of  tons  necessary  to 
lay  5  rods  of  single  track. 

23.  How  much  does  an  architect  receive,  at  4*  %,  for  the 
plans  of  a  house  that  cost  $8350? 

24.  A  man's  salary  is  $150  per  month.  He  spends  40  %  of 
it  for  clothing  and  other  expenses.  How  much  does  he  save 
in  a  year  ? 

25.  A  man  purchases  80  acres  of  land  for  $6400,  and  sells 
them  at  25%  gain.     How  much  does  he  receive  per  acre? 

26.  Frank  Stewart  borrows  $250  Sept.  15,  1906,  at  6% 
interest.    Find  the  amount  of  the  note  if  paid  March  15, 1908. 

27.  Find  the  area  in  acres  of  a  street  7  miles  long  and 
66  feet  wide. 


GENERAL   REVIEW  161 

28.  A  town  lot  is  43  ft.   3  in.   wide  and  120  ft.   deep. 

How  much  is  it  worth  at  75  $  per  square  foot? 

29.  A  western  farmer  harvests  8960  bu.  wheat  from  a 
field  320  id.  long  and  160  rd.  wide.  If  he  sells  the  wheat  at 
60^  per  bushel,  how  much  does  he  realize  from  each  acre? 

30.  In  1  hour  20  minutes  and  40  seconds,  a  train  travels 
60  miles.  At  that  rate  how  long  would  the  train  be  in 
traveling  1200  miles? 

31.  The  average  wages  of  a  steel  mill  employing  3000 
men  are  $2.50  per  day.  If  a  10%  reduction  in  wages 
is  made,  how  much  per  day  will  the  company's  pay  roll  be 
reduced? 

32.  In  a  certain  class  the  salary  of  the  teacher  for  a  year 
is  $500.  The  books  and  supplies  cost  $90.65 ;  fuel,  $40  , 
repairs  and  other  expenses,  $75.30.  There  are  35  pupils  in 
the  class.     Find  the  average  cost  per  pupil  for  the  year. 

33.  Reduce  to  improper  fractions:  6.25;  3.375;  4.66| ; 
and  2.05. 

34.  If  it  costs  $72  to  carpet  a  room  18  ft.  long  and  18  ft. 
wide,  how  much  will  it  cost  to  carpet  a  room  36  ft.  long 
and  36  ft.  wide,  with  the  same  quality  of  carpet? 

35.  Mt.  Rainier  is  14,363  ft.  high.  Reduce  the  height  to 
miles  and  the  fractions  of  a  mile. 

36.  How  many  cubic  inches  are  there  in  a  bin  9  ft.  7  in. 
long  by  8  ft.  3  in.  wide  and  4  ft.  9  in.  deep?  how  many 
cubic  feet? 

37.  A  grocer  bought  225  bu.  apples  at  $.50  per  bushel. 
He  sold  150  bu.  at  $.75  per  bushel.  The  remainder,  which 
were  damaged,  he  sold  at  $  .40  per  bushel.  Did  he  gain  or 
lose  and  what  per  cent? 

HAM.    COMPL.     ARITI1. 11 


102  GENERAL  REVIEW 

38.  What  is  331%  of  24?  of  84.80?  of  862.50? 

39.  A  piece  of  land  30  rods  wide  and  480  rods  long  was 
sold  at  862.50  per  acre.     Find  the  amount  of  the  sale. 

40.  Time,  3  months;  rate  of  interest,  5  % ;  money  borrowed, 
8100.     Find  amount  to  be  paid. 

41.  If  f  of  a  bushel  of  potatoes  cost  8.40,  how  much  will 
1\  bu.  cost? 

42.  A  piece  of  land  40  rods  long  in  the  form  of  a  rec- 
tangle contains  5  acres.     Find  its  width  in  rods. 

43.  A  farmer  sold  12|  acres  of  land  at  855|  per  acre. 
How  much  did  he  receive  for  the  land? 

44.  Houser  Brothers  sold  the  following  bill  of  goods  to 
William  Pool : 


12  lb.  sugar 

10  cans  tomatoes 

@  8.061 
@8.15 

6  lb.  rice 
11  lb.  prunes 
2  pair  boots 
1  overcoat 
1  pair  shoes 

@  I.07J 

@  8.071 
@  83.50 
@  813.50 
@  84.00 

Pool  at  the  same 

time  sold  Houser  Brotl 

85  bu.  potatoes 
50  bu.  corn 
16  lb.  butter 

@8.65 
@  8.421 

@$.24 

10  lb.  butter 

@  8.28 

Houser  Brothers  gave  Mr.  Pool  the  balance  in  cash.     Make 
out  the  account. 

45.    A  painter  worked    17^    days.     After  spending  |-  of 
his  wages  for  board  he  had  815  left.     Find  his  daily  wages. 


GENERAL   REVIEW  163 

46.  I  owe -Frank  Morrison,  the  grocer,  $32.50  and  pay  him 
$23.75.  Write  the  receipt  that  Mr.  Morrison  should  give 
me. 

Note. —  When  a  debt  is  not  paid  in  full,  the  receipt  should  read  "  On 

account." 

47.  A  cellar  24  ft.  by  32  ft.  is  to  be  excavated  to  an 
average  depth  of  5|  ft.  Find  the  number  of  cubic  yards  to 
be  removed. 

48.  Express  22|  yards  as  rods,  feet,  and  inches. 

49.  The  width  of  a  rectangle  is  20  rods  and  the  area 
is  560  square  rods.     Find  the  length. 

50.  What  is  the  difference  between  a  square  and  a  rec- 
tangle ? 

51.  Give  the  rule  for  rinding  percentage.  On  what  is  gain 
or  loss  always  reckoned  ? 

52.  A  man's  farm  and  personal  property  cost  $5600.  The 
first  year  he  cleared  12|  %  of  the  money  invested.  The  sec- 
ond year,  on  account  of  floods,  he  lost  5  %  of  the  cost  of  the 
property.     How  much  was  his  gain  in  the  two  years? 

53.  Of  a  bill  of  $155  sent  to  a  collector,  80%  was  col- 
lected and  the  collector  retained  $12.40.  What  per  cent  did 
he  charge  for  collecting? 

54.  A  boy  receives  $1.20  per  day  and  a  man  $2.50  per 
day.  How  long  will  it  take  the  boy  to  earn  as  much  as  the 
man  can  earn  in  30  days? 

55.  The  perimeter  of  a  rectangle  is  72  rods.  The  width 
is  12  rods.     Find  the  length. 

56.  Estimating  that  300  cu.  ft.  of  air  is  required  for  each 
pupil,  how  many  pupils,  including  the  teacher,  should  occupy 
a  room  40  ft,  long,  30  ft,  wide,  and  12  ft.  high? 


164  GENERAL  REVIEW 

57.  Divide  one  thousand  and  one  thousandth  by  one 
and  one  thousandth. 

58.  What  is  the  interest  on  $375  for  270  days  at  6  %  ? 

59.  Reduce  f  of  a  mile  to  lower  denominations. 

60.  A  boy  deposited  half  of  his  money  in  the  savings 
bank;  ^  of  the  remainder  he  spent  for  clothes;  and  he  had 
$3  remaining.     How  much  had  he  at  first  ? 

61.  Reduce  .025  cwt.  to  lower  denominations. 

62.  A  man  bought  two  city  lots  costing  him  -13500  and 
$  4100  respectively.  He  sold  them  at  a  gain  of  25  %.  What 
was  the  gain  in  dollars  ? 

63.  How  many  gallons  of  water  will  a  tank  contain  that 
is  11  ft.  long,  3^  ft.  wide,  and  4  ft.  deep  ? 

64.  A  barn  floor  is  20  ft.  wide  and  45  ft.  long.  How 
much  will  it  cost  to  cover  it  with  plank  2  inches  thick  at  1 20 
per  thousand  board  feet  ? 

65.  Divide  j  by  f  of  f . 

66.  John  and  James  have  together  165  acres  of  land,  but 
James  has  twice  as  many  acres  as  John.  How  many  acres 
has  each  ? 

Suggestion.  — 165  acres  =  twice  John's  +  once   John's  or  3  times 
John's. 

67.  What  fractional  part  of  a  day  are  10  hours,  50  min- 
utes, 40  seconds? 

68.  Divide  nine  ten-thousandths  by  one  hundred  twenty- 
five  thousandths. 

69.  What  is  the  interest  on  $  180  for  4  yr.  8  mo.  at  5f  %  ? 

70.  I  made  $1.95  by  selling  15  dozen  eggs  at  $.31  per 
dozen.     What  was  the  cost  of  the  eggs  per  dozen  ? 


GENERAL   REVIEW  165 

71.  Find  the  net  proceeds  from  the  sale  of  145  books,  at 
|2  each,  on  which  a  commission  of  33^%  is  paid. 

72.  A  father  divided  his  farm  of  202  A.  16  sq.  rd.  equally 
among  his  four  sons.     How  many  acres  did  each  receive  ? 

73.  .21  of  a  mile  is  equal  to  how  many  feet? 

74.  An  automobile  that  cost  $2675  was  sold  at  a  loss  of 
28  %.     For  how  much  was  it  sold  ? 

75.  What  is  the  cost  of  18  planks  20  ft.  long,  12  in.  wide, 
and  2  in.  thick,  at  120  per  M?  , 

76.  \  of  7  is  what  part  of  9  ? 

77.  f  of  a  farm  is  worth  $7500.     What  is  20%  of  the 
farm  worth  ? 

78.  What  is  the  cost  of  a  car  load  of  bituminous  coal  weigh- 
ing 84,000  pounds  at  $2.65  per  ton  ? 

79.  A  farm  in  the  form  of  a  rectangle  containing  120  acres 
is  60  rods  wide.     How  long  is  it  ? 

80.  Express  decimally  the  quotient  of  £  ■*-  .35. 

81.  If  |  of  a  ton  of  hay  is  worth  $12,  how  much  are 
33,000  pounds  of  hay  worth  ? 

82.  What  is  the  value  of  a  pile  of  4-foot  wood  48  ft.  long 
and  6  ft.  high,  at  $4.50  per  cord  ? 

83.  A  dairyman  owns  a  cow  that  averages  3  gal.  2  qt. 
1  pt.  of  milk  daily.  If  he  sells  the  milk  at  $.06  per  quart, 
how  much  will  he  realize  from  the  cow  during  the  month 
of  May  ? 

84.  I  can  buy  an  automobile  at  one  store  for  $3000,  with 
discounts  of  25  %,  10  %;  or  at  another  store  for  $3000  with 
only  one  discount  of  35%.      Which  is  the  cheaper? 


PART   II  — SEVENTH    YEAR 
BILLS  AND  ACCOUNTS 

RECEIPTS 

John  Bentz  rents  a  house  in  Boston,  Mass.,  from  James 
Smith  for  one  year  for  $240,  rent  payable  the  first  day  of 
each  month  in  advance. 

1.  Every  receipt  should  state  (1)  the  place  and  date  of  payment; 
(2)  who  pays  the  money  ;  (3)  who  receives  the  money;  (4)  for  what  the 
money  is  paid ;   (5)  the  amount  both  in  figures  and  in  writing. 

2.  Every  receipt  in  full  should  state  in  full  to  date. 

Write  the  receipt  given  Mr.  Bentz  for  September's  rent. 


1.  Providing  John  Bentz  fails  to  pay  the  rent  for  August 
when  due,  but  pays  on  September  1  the  rent  for  both 
August  and  September,  write  the  proper  receipt. 

2.  Write  the  receipt  for  the  tuition  for  the  term  of  your 
school  that  any  non-resident  pupils  would  have  to  pay. 

Write  the  receipt  in  full  to  date  for  each  of  the  follow- 
ing bills  which  I  owe : 

166 


ORDERINCx   GOODS  167 

3.  John  Thompson  for  milk,  $6.75. 

4.  Frank  Jones  for  coal,  $16.85. 

5.  Smith  &  Co.  for  books,  $3.75. 

ORDERING   GOODS 

These  forms  of  orders  should  be  studied  carefully,  as  they 
come  into  almost  daily  use  in  business  life. 

A 


FURNEE    AND    KENNERDELL,  KlTTANN.NG,    Pa.,    fat.     W,     /  <?  0  7 . 

Booksellers. 

(X  %>vEA,Lean-  fSaok,  (HvwLJbaAvy, 

/OO  IM-a^kinato-n  ^qioaA&,  cftzw-  1fr>ik- 

Jbe,av  cfvi&: 

ffl&a&t  Qs/i  ifi  at  &n&&  6-if  S>&n/n^/iflv-ayyvuv  ^vt^Ujkt  : 

300  Rois,  §'vlr,i&v&. 

"Uoii  1  1   1 1  ;ily, 

~j  :<sWiz&  V*  fCzvm&'uLzli. 


B 


Sh^rCkiirv,  i'a.,  fan.  /,  /907- 

&0  BcKjCfQ,  ¥  Buhl, 

(luecjh&wif,  <Pa. 

fCvyidtu  a&nd  6-1/  (I dam*,  €<xJja,xz-io,  th&  foltoiv-tna, 

4.&V  &a'mAl&,  and  &kai<fb  tk&  <uvm,e,  to-  inAf  amount. 

fO  ltd.    ot  vikkon,    at  $0.50 

/2  ud.    ot  dve&i-  cjoodos,   at    $/.2<5 

(nil*.)  &ka*.  Ci.  dtttte,. 


a& 


168 


BILLS  and  accounts 


1.  Make  out  an  order  to  each  of  the  various  schoolbook 
companies  for  the  books  you  are  studying. 

2.  Make  out  an  order  to  McCreery  &  Co.  of  New  York, 
for  some  goods  to  be  sent  to  you  C.O.D.  (cash  on  delivery). 


RECEIPTED    BILLS 

Study  the  following  : 


New  Castle,  Pa.,  ftfay  /,  /<?07. 

TfK.  yaAn&Q,  &ux,nt, 

2V-  (HounUf  Line,  dt. 

Bou^bt  of  JOHN    KNOX    &  SON, 
196  E.  Washington  St., 

FANCY    GROCERS. 

TERMS:  &a^lh 

/407. 

/ 

20 
25 
27 

KM.  Mt,                                 f/.50 
20  16-.  £/iM. nutated  c/^^a-t,         6}£$ 
10  6-tc.  gotaUe*,                          60 1 
6  10-.  ftonesy,                                 20$ 

R&&&lv-uL  S'axpn^eml ,  THaif,  10,   07- 
jlo-Artv  /Cru>?c  If  ofon. 

Jch  W-at^yyv. 

// 

/ 
6 
/ 

50 
30 
00 
20 

fO 

00 

Observe : 

1.    The  place  and  date  of  sale.     2.   The  names  of  the  buyer 
and  the  seller.    3.  The  name,  quantity,  and  price  of  each  arti- 
cle.    4.    The  entire  amount  of  each  separate  item.     5. 
total  amount  of  the  bill.     6.    The  receipt  of  the  bill. 


The 


RECEIPTED   RILLS 


it;o 


A  bill  is  a  written  statement  in  detail  of  goods  sold  or  of 
services  rendered. 

A  bill  is  receipted  when  the  words  "Received  payment" 
are  written  at  the  bottom  of  the  bill,  either  by  the  seller  or 
by  some  person  authorized  by  him. 

Note.  —  When  the  person  authorized  signs  the  name  of  the  seller,  he 
should  always  write  on  the  next  line  below  the  word  "  by  "  or  "  per  "  and 
his  own  name  or  initials. 

When  a  person  purchases  anything  on  time,  the  purchaser  is  called  a 
debtor. 

When  the  seller  extends  the  time  of  payment  to  any  one,  the  seller  is 
said  to  give  credit,  and  therefore  is  called  a  creditor. 


Some  abbreviations  used  in  business: 
Acct.  %,       account         mdse., 


Amt., 

bal., 

Co., 

Cr., 

Dr., 

do.  CO, 


amount 

balance 

company 

creditor 

debtor 

the  same 


No.  (#), 

paymt., 

pd., 

per, 

pc, 

rec'd, 


merchandise 
number 
payment 
paid 

by 

piece 
received 


The  symbol  #  means  pounds  when  placed  after  a  number; 
but  number  if  placed  before  a  number. 

Thus  6  j  means  6  pounds  but  *6  means  Number  6. 

Make  receipted  bills  for  the  following  transactions,  per- 
forming all  necessary  operations : 

l.  Carter  Bros.,  Elkins,  W.  Va.,  purchase  from  Bindley 
Hardware  Co.,  Pittsburg,  Pa.,  the  following:  3  dozen 
locks  @  $4.80,  67  kegs  of  nails  @  $4.10,  6  dozen  lanterns 
@$6.25,  1300  feet  steel  tracks  @  16^,  and  7  lawn  mowers 

@  $4.25. 


170  BILLS   AND   ACCOUNTS 

2.  John  Dunn  &  Son,  Akron,  Ohio,  bought  from  Thomas 
Townsend  &  Company,  Cleveland,  Ohio,  36  barrels  of  flour 
@  $4.80,  4  boxes  of  prunes  @  $1.65,  500  pounds  of  coffee 
@  llf^,  7  boxes  of  yeast  @  75^,  50  pounds  of  Huyler's 
cocoa  @  32^. 

3.  James  Brown,  Lincoln,  Neb.,  purchases  from  May  & 
Co.,  St.  Louis,  Mo.,  22  bunches  bananas  @  $1.75,  32  boxes 
oranges  @  $3.15,  17  boxes  lemons  @  $'2.80,  29  crates  cran- 
berries @  $2.25,  6  boxes  grape  fruit  @  $2.90,  and  35  bbl. 
apples  @  $2.75. 

4.  James  Sweitzer,  Peoria,  111.,  bought  from  Swift  &  Co., 
Chicago,  1587  pounds  of  dressed  beef  @  7-^,  267  pounds  of 
mutton  @  9^,  933  pounds  of  pork  @  5|^,  and  180  pounds 
of  lard  @  12£ 

5.  Lyle  Bros.  &  Co.,  Dubuque,  la.,  bought  of  the  De- 
laney-Brown  Lumber  Co.,  Grand  Rapids,  Mich.,  28215  feet 
oak  boards  at  $32  per  M.,  147820  feet  hemlock  at  $27  per 
M.,  92629  feet  No.  1  white  pine  at  $60  per  M.,  63605  feet 
poplar  boards  at  $35  per  M. 

Note.  —  $32  per  M.  equals  $.032  per  board  foot. 

6.  Mrs.  James  Thorpe  bought  of  B.  Altman  &  Co.,  New 
York,  1  pair  gloves  at  $2.75,  5  yd.  ribbon  at  39^  a  yard, 
I  dozen  handkerchiefs  at  25^  each. 

ACCOUNTS 

In  the  study  of  bills  we  simply  found  how  much  the 
debtor  owed  to  the  seller,  or  what  one  party  owed  to  another 
for  services  rendered. 

In  an  account  we  have  a  business  transaction  covering  a 
period  of  time  in  which  there  is  both  a  debtor's  bill  and  a 
debtor's  payments. 


ACCOUNTS 


171 


Form  of  Account 


Pittsburg,  Pa.,    TTicwf  /,  /c/07. 

Plv.  cfawvu&f-  BarucL, 

U^/lt.alVna,   Z&.  Ucl: 

Jo   JOSEPH    HORNE    CO.,    Dr. 

3v. 

Ofa. 

/ 

&o  CLmawnt  ieM,deA,&cL 

$ffO 

29 

ti 

fO 

"   20  yd.  ^Ifc             @  $f.  50 

SO 

00 

1 1 

25 

"  2  Ladies'  &uvU  @  ¥-5.00 

qo 

00 

//- 

28 

7 

80 

238 

oq 

// 

/¥■ 

ISu  &<x&lv 

fOO 

00 

// 

2V- 

6o 

00 

/60 

00 
09 

78 

Note. — If  the  above  balance  were  paid  in  full  May  1,  the  words 
"Received  Payment "  would  be  written. 

Joseph  Horne  Co., 

Per 


It  is  customary  for  the  creditor  to  send  an  itemized  account 
to  the  debtor.  If  it  is  not  paid,  another  form  of  bill  called 
a  statement  is  sent  and  contains  only  these  words  :  "  To 
account  rendered"  or  "To  Mdse."  followed  by  the  amount. 

In  the  above  account,  what  shows  that  there  was  a  previous 
transaction  ? 


172  BILLS  AND  ACCOUNTS 

Render  the  following  statements: 

1.  Jan.  31, 1906,  the  debits  and  credits  of  George  Weil  in 
account  with  John  Wanamaker,  Philadelphia,  Pa.,  were  as 
follows : 

Debits 
Jan.  1,  To  account  rendered,  1295.63, 
Jan.  7,  To  3  overcoats  @  $32, 
Jan.  12,  To  7  yd.  dress  goods  @  $4.75, 
Jan.  20,  To  1  suite  of  furniture,  $185. 

Credits 
Jan.  5,  By  cash,  $250, 
Jan.  20,  By  note  for  30  days,  $200. 
Find  balance  due  Wanamaker. 

2.  Nov.  30, 1905,  the  debits  and  credits  of  R.  D.  McClurg, 
with  Stevenson  &  Co.,  Richmond,  Va.,  were  as  follows: 

Debits 
Nov.  1,  To  account  rendered,  $86.25, 
Nov.  10,  To  12  cases  corn  @  $1.65, 
Nov.  19,  To  4  bbl.  sugar,  1692  lb..  @  4j£ 
Nov.  22,  To  75  lb.  dry  beef  at  19  £ 

Credits 
Nov.  5,  By  cash,  $85, 
Nov.  30,  By  note  for  balance  due. 

3.  On  Oct.  31,  the  account  of  Win.  B.  Eager  with  H.  A. 
Soltori,  New  York,  was  as  follows : 

Debits  Credits 

Oct.  2,  To  mdse.,  $93.37,  Oct.  10,  By  cash,  $80, 

Oct.  8,  To  mdse.,  $107.92,  Oct.  20,  By  30-day  note, $100. 

Oct.  21,  To  mdse.,  $21.58.  Oct.  31,  By  cash,  $25. 


LEDGER   ACCOUNTS 


173 


LEDGER  ACCOUNTS 

The  orders  or  payments  when  received  by  a  firm  are  first 
put  in  a  day  book  in  the  order  of  their  arrival.  Each  person's 
or  firm's  business  is  then  placed  in  a  book  called  the  ledger, 
which  is  ordinarily  balanced  each  month  or  when  an  account 
is  paid. 

A  ledger  account  is  headed  by  the  name  of  the  person  and 
arranged  so  that  the  purchases  appear  on  the  left  side  as  debits, 
and  the  payments  or  services  rendered  appear  on  the  right  side 
as  credits. 

The  statement  of  account  as  given  on  page  171  is  simply  a 
copy  of  Mr.  Bond's  ledger  account  with  Joseph  Home  Co. 

The  following  form  shows  a  balanced  ledger  account  at  the 
close  of  the  month  with  James  Roberts,  the  balance  being 
brought  down  to  continue  the  account  into  the  next  month. 


Dr. 

$awve<a/ 

Rok&itb 

Cr. 

1907 

1907 

Feb. 

1 

Bal.  bro't  f'w'd 

$19 

30 

Feb. 

6 

Cash 

6* 

$30 

00 

it 

2 

Lumber 

2* 

19 

80 

u 

11 

Dray  age 

46 

15 

75 

(i 

4 

Cement 

8 

40 

50 

(I 

18 

Dray  age 

60 

8 

50 

u 

5 

Sand 

Lfi 

9 

50 

l( 

22 

Drayage 

70 

26 

50 

(< 

9 

Tile 

30 

15 

70 

11 

25 

Cash 

71 

82 

50 

(( 

13 

Plaster 

5ii 

56 

30 

(( 

28 

Balance 

38 

75 

1( 

18 

Sewer  pipe 

60 

20 

90 

l( 

26 

1 

Lumber 

Bal.  bro't  f'w'd 

75 

20 
202 

00 
00 

75 

202 

00 

Mch. 

38 

l.    What  debts  in  this  ledger  account   did   Mr.  Roberts 
incur  during  the  month  ?     What  payments  did  he  make  ?  . 

*  These  numbers  refer  to  the  pages  in  the  day  honk  in  which  the  accounts 
are  found. 


174  BILLS  AND  ACCOUNTS 

2.  Find  the  sum  of  the  debits  and  the  sum  of  the  credits. 
Does  the  difference  equal  the  balance,  §38.75? 

3.  Is  the  balance  in  favor  of,  or  against  Mr.  Roberts  ? 

4.  Had  the  balance  been  in  favor  of  Mr.  Roberts,  on  which 
side  would  it  have  been  entered  ? 

5.  How  do  you  determine  on  which  side  to  enter  the 
balance  ?    on  which  side  to  bring  down  the  balance  ? 

To  foot  a  ledger  is  to  add  and  set  down  (usually  in  pencil) 
the  total  debits  and  credits  of  the  accounts. 

Test.  — When  the  footing  of  one  side  equals  the  footing  of  the  other 
side,  the  account  is  in  balance. 

Written  Work 
The  day  book  shows  the   following   sales   and   receipts. 
Make  a  ledger  for  the  year,  enter  each  item,  foot  and  close 
the  accounts. 

1.  William  Stone. 

Debits.  —  Feb.  1,  cook  stove,  $ 22  ;  Feb.  4,  40  lb.  nails, 
$2.40;  Feb.  5,  heater,  $75.70 ;  Feb.  12,  tin  roofing,  $79.08; 
Feb.  19,  hardware,  $  14 ;  Feb.  23,  lime  and  cement,  $50.70; 
Feb.  28,  tile,  $  22. 

Credits. —Feb.  1,  sand,  $15  ;  Feb.  4,  drayage,  $9.50  ; 
Feb.  12,  cash,  $50  ;  Feb.  16,  lumber,  $74.25;  Feb.  25,  cash, 
$20;  Feb.  28,  cash,  $105. 

2.  Morris  Brown  &  Co. 

Debits.  —Apr.  4,  mdse.,  $15.90  ;  Apr.  5,  lumber,  $190.72 ; 
Apr.  11,  mdse.,  $23.15;  Apr.  12,  wagon,  $90;  Apr.  27, 
mdse.,  $20.70;  surrey,  $129.70;  May  7,  mdse.,  $40.05; 
May  12,  cash,  $  100  ;  May  20,-  lumber,  $  189. 

Credits.  —Apr.  10,  labor,  $129.71  ;  Apr.  14,  cash,  $  75  ; 
Apr.  21,  labor,  $29.70  ;  Apr.  28,  cash,  $147  ;  May  7,  labor, 
$270.10;  May  19,  stone  work,  $175.39;   May  28,  cash,  $70. 


DENOMINATE   NUMBERS 

We  measure  the  quantity  of  anything  by  finding  how 
many  times  it  contains  some  unit  of  the  same  kind,  called 
the  unit  of  measure. 

Thus,  the  number  of  bushels  in  a  load  of  apples  is  found  by  seeing 
how  many  times  it  contains  the  unit  of  measure,  1  bushel. 

A  denominate  number  is  a  concrete  number  whose  unit  is 
a  measure  established  by  custom  or  law  ;  as,  5  yards  or  8 
bushels.  In  these  numbers  1  yard  and  1  bushel  are  the 
units  of  measure. 

A  simple  denominate  number  is  a  number  of  one  denomi- 
nation ;  as,  3  feet,  5  pecks. 

A  compound  denominate  number  is  a  number  composed  of 
two  or  more  denominations  that  express  one  quantity;  as, 8 
yards,  2  feet,  3  inches  (length). 

REDUCTION 
.  Reduction  of  denominate  numbers  is  changing  their  form 
without  changing  their  value  ;  thus, 

2  bu.  =  8  pk.  =  64qt. 
or,  16  qt.  =  2  pk.=  .5  bu. 

l.  Review  thoroughly  these  tables:  Liquid  Measures; 
Dry  Measures  ;  Measures  of  Length  ;  Avoirdupois  Weight ; 
Troy  Weight ;  Time  Measures ;  Stationers  Measures ; 
Counting. 

Note.  — The  other  tables  of  denominate  numbers  are  found  on  pages 
433  to  436. 

175 


176  DENOMINATE   NUMBERS 

2.  Change  61  qt.  to  bushels  ;  to  pints. 

3.  How  many  pecks  in  \  bu.  ?  3  bu.  ?  1|  bu.  ? 

4.  How  many  days  from  June  28  to  October  1  ? 

5.  Express  5  yards  as  feet;    as  the  fraction  of  a  rod. 

6.  How  many  rods  equal  27|  yards  ?  49^  yards  ? 

7.  Change  $2.50  to  mills;  to  dimes. 

8.  Change  1.3  T.  to  pounds. 

9.  Express  27  pecks  as  bushels  ;  as  quarts. 

10.  How  many  ounces  (avoir.)  equal  |  lb.  ?    2.5  lb.  ?   4| 
lb.  ?  7 J  lb.  ? 

11.  If  a  ring  is  18  carats  fine,  what  part  of  it  is  pure  gold  ? 

12.  Express  in  minutes  1.5  hr. ;  1.75  hr. ;   3^  hr. 

13.  Express  in  feet  1|  rd.;  1\  rd.;  8  yd.;  and  5|  yd. 

14.  How  many  minutes  equal  720  seconds  ?  3600  seconds'.'' 

15.  How  many  days  is  it  from  January  28,  1908  to  March 
5,  1908  ? 

16.  If  a  man  works  8  hours  a  day,  how  many  minutes  does 
he  work  ?     How  many  minutes  equal  9  hours  ? 

17.  How  many  sheets  of  paper  are  there  in  2  reams  of 
paper  ?   in  5  reams  ? 

18.  I  bought  2  gross  of  lead  pencils.      How  many  lead 
pencils  did  I  buy  ? 

19.  If  a  horse  eats  10  quarts  of  oats  a  day,  how  long  will 
5  bushels  of  oats  last  ? 

20.  How  many  dozen  equal  180  things?  how  many  gross? 

21.  How  many  days  is  it  from  Memorial  Day  (May  30) 
to  the  fourth  of  July  ? 

22.  What  is  the  perimeter  of  square  that  is  3.6  ft.  on  a 
side  ? 


REDUCTION  177 

23.  How  many  pecks  does  a  3-bushel   bag   hold  ?   a    2- 
bushel  bag  ?  a  5-bushel  box  ? 

24.  A  bushel  of  wheat  weighs  GO  lb.      How  many  bushels 
are  there  in  a  ton  of  wheat  ? 

25.  How    many   feet    are   there    in    125  yards  ?  in  120 
inches  ? 

26.  Change  5  T.  4  cwt.  to  tons  ;  to  pounds ;  to  hundred- 
weight. 

27.  Find  the  weight  in  ounces  of  a  dozen  teaspoons,  each 
weighing  12  pennyweights. 

Changing  to  smaller  denominations. 

Written  Work 

1.  Change  7  gal.  3  qt.  1  pt.  to  pints. 

Since  there  are  8  pt.  in  1  gallon,  in 

7  gal.  =  7  X  8  pt.  =  56  pt.       7  gal.  there  are  7  times  8  pt.,  or  56  pt. 

3  qt.   =3x2  pt.  =     6  pt.       Since  there  are  2   pt.  in  1  qt.,  in   3  qt. 

^     t  _     ]  pt,        there   are    3    times    2    pt.,    or    6    pt. 

=^-i — 5 1 — 1 7TTT- —      Hence,  in  7  gal.  3  qt.  1  pt.  there  are  56 

7  gal.  3  qt.  1  pt.  =  03  pt.      pt  +  6  pt    *  l  pt  *or  63  pt 

2.  A  dairyman  delivered  to  his  customers  in  one  morning 
19  gal.  3  qt.  1  pt.  of  milk.   Find  the  number  of  pints  delivered. 

19,  number  of  gal. 

—  The    product    is    numerically  the   same 

7"  whatever  number  is  the  multiplier.     Thus, 

+  3  4  X  19  =  19  x  4;  hence  to  shorten  the  work 

79,  number  of  qt.  4  and  2   may  be   regarded   as   multipliers, 

9  although  in  the  explanation  it  must  be  re- 

■z-^  membered  that  4  qt.  and  2  pt.  are  really 

the  multiplicands. 
+  1 
159,  number  of  pt. 

MAM.    COMPL.    AR1TH.  —  12 


178  DENOMINATE   NUMBERS 

Reduce  : 
3.    28  bu.  3  pk.  to  quarts.  8.    16  T.  15  cwt.   85  lb.  to 


27  gal.  1  qt.  to  pints.  pounds. 

10  da.  7  hr.  to  hours.  9'    1  sokr  ?ear  to  hours 


4. 
5. 

6.    8  mi.  80  rd.  to  rods. 

A ,  t      n  i      on     •      +~         11.    25  rd.  3  yd.  2  ft.  to  feet. 
15  da.  9  hr.  20  mm.  to  J 


10.    12  fathoms  5  ft.  to  inches. 


7 


minutes.  12.    5  knots  1050  ft.  to  feet. 

13.  11  lb.  8  oz.  to  ounces  (avoir.). 

14.  _5_  0f  a  ton  to  a  hundredweight  and  pounds. 

T5,  T.  =  T5?  of  20  cwt.  =  6i  cwt. 
£cwt.  =  i  of  100  1b.=  25  1b. 
T56  of  a  ton  =  6  cwt.  25  lb. 

Change: 

15.  If  lb.  to  ounces. 

16.  1|  bu.  to  pints. 

17.  2  mi.  4020  ft.  to  inches. 

18.  |  mi.  to  rods. 

19.  |  long  ton  to  hundredweight  and  pounds. 

20.  |  common  years  to  days,  hours,  etc. 

21.  In  an  automobile  race  the  fastest  machine  ran  |  of  a 
mile  in  36  seconds.  Find  the  number  of  feet  it  ran  per 
second. 

22.  Change  .75  week  to  days,  etc. 

23.  School  is  in  session  4.25  hours.  Find  the  number  of 
minutes  it  is  in  session. 

24.  James  lives  1.85  miles  from  school.  Find  the  number 
of  feet  he  walks  to  school. 


REDUCTION  179 

Changing  to  larger  denominations. 

Written  Work 

1.  An  ice  cream  dealer  retailed  in  one  day  127  pints  of 
ice  cream.     How  many  gallons,  quarts,  etc.,  did  he  sell  ? 

2  )127,  no.  of  pt.  Since  2  pt.  =  1  qt.,  127  pt.  =  63 

,.  ,.,,  <•  ,    1  qt.  and  1    pt.  over.      Since  4   qt. 

4)b3,  no.  of  qt.  +  1  pt.  *  1  ^  ^  =  lg  ga]  and  g  qt 

15,  no.  of  gal.  +  3  qt.  over      Hence>  127  pt  _  15  gal#  3 

117  pt.  =  15  gal.,  3  qt.,  1  pt.      qt.  i  pt. 

Note.  — The  dividend  and  divisor  are  regarded  as  abstract  numbers. 
Do  not  read  127  pt.  •*■  2  =  63  qt.     Such  a  statement  would  be  absurd. 

(  hange: 

2.  225  qt.  to  gallons,  etc.      7.   5675  sec.  to  minutes,  etc. 

3.  2550  qt.  to  barrels,  etc.     8.   75000  in.  to  miles,  etc. 

4.  1463  pk.  to  bushels,  etc.     9.  36481.62  ft.  to  leagues,  etc. 

5.  15000  min.  todays,  etc.  10.   175680  oz.  to  long  tons,  etc. 

6.  3184  in.  to  rods,  etc.      11.  9049  in.  to  rods,  etc. 

12.  3  qt.  1  pt.  to  the  decimal  of  a  gallon. 

2)1.0,  no.  pt. 

•  5  Since  2  pt.  =  1  qt.,  1  pt.  =  .5  qt.;  3  qt. 

3.  +  .5  qt.  =  3.5  qt.      Since  4   qt.  =  1   gal., 

4  )^5,  no.  qt.  3-5  ^  =  -875  Sal- 

.875,  no.  gal. 

Change : 

13.  45  yd.  .6  ft.  to  the  decimal  of  a  mile. 

14.  6  cwt.  8  oz.  to  the  decimal  of  a  ton. 

15.  |  ft.  to  the  common  fraction  of  a  yard. 

1  ft.  =  4  yd. 

1  ft.  =  §  of  i  yd.,  or  f  yd. 

16.  |  in.  to  the  fraction  of  a  foot  ;  of  a  yard. 

17.  12  oz.  to  the  fraction  of  an  avoirdupois  pound. 


180  DENOMINATE   NUMBERS 

18.  240  rd.  to  the  fraction  of  a  mile. 

19.  The  winner  in  an  automobile  race  won  in  21  hr.  3 
min.  3.6  sec.     What  decimal  of  a  day  did  it  take  ? 

20.  How  much  did  a  merchant  receive  for  3  barrels  (42 
gallons  each)  9  gallons  3  quarts  of  oil,  retailed  at  15  cents 
per  gallon  ? 

21.  A  grocer  bought  150  bushels  of  potatoes  at  60^  a 
bushel.  He  lost  ^  of  them  by  freezing,  and  retailed  the 
remainder  at  10^  a  half  peck.     How  much  did  he  gain  ? 

22.  How  many  boxes,  each  holding  a  quart,  can  be  filled 
from  3  bu.  1  pk.  7  qt.  of  blackberries  ? 

23.  At  $2.88  a  bushel,  how  many  quarts  of  chestnuts  can 
be  bought  for  $13.50? 

24.  What  is  the  profit  on  9  quires  of  paper,  bought  at 
$2.40  a  ream  and  sold  at  a  cent  a  sheet  ? 

25.  A  rural  mail  carrier's  route  is  21  miles  176  rd.  4  yd. 
in  length.  Find  the  number  of  feet  he  travels  in  one  delivery 
of  mail. 

26.  A  fruit  grower  sold  in  one  season  23  bu.  crates  of 
cherries  at  10  cents  per  basket;  and  45  bu.  crates  and  17 
baskets  of  strawberries  at  13  cents  per  basket.  Find  the 
amount  of  the  sales. 

A  crate  contains  32  baskets. 

27.  A  milk  dealer  put  his  milk  in  pint  bottles.  Find  the 
number  of  bottles  delivered  in  one  evening  if  he  sold  23  gal., 
3  qt.,  and  1  pt. 

28.  How  many  4-ounce  packages  of  soda  can  be  put  up 
from  IT.,  3  cwt.,  and  75  lb.  of  soda  ? 

29.  A  huckster  bought  3  barrels  of  apples,  each  containing 
2|  bushels,  for  $8.25  and  retailed  them  at  15^  a  half  peck. 
Find  his  profits. 


FOREIGN   MONEY  181 

30.  Find  the  length  of  ;i  double-track  railroad  laid  with 
1640  rails,  each  30  feet  in  length. 

31.  An  ocean  steamer  in  making  a  certain  trip  consumed 
l'.>20  tons  of  coal.  If  the  time  was  6  days,  5  hours,  and  8 
minutes,  find  the  average  number  of  pounds  consumed  per 
minute. 

32.  The  report  of  a  cannon  was  heard  1  minute  5  sec- 
onds after  it  was  discharged.  If  sound  travels  1120  feet  per 
second,  how  many  miles,  rods,  etc.,  was  the  hearer  from  the 
cannon  ? 

33.  A  pupil  pays  845  tuition  in  a  term  of  9  months  of  20 
days  each,  and  is  absent  from  school  16  days.  Counting 
6  school  hours  to  a  day,  find  the  amount  of  tuition  lost  to 
him  by  his  absence. 

FOREIGN  MONEY 
English  Money 
The  standard  unit  of  English  money  is  the  pound,  $4.8665. 

4  farthings  (far.)  =  1  penny  (</.) 
12  pence  =  1  shilling  (s.) 

20  shillings  =  1  pound  (£),  or  sovereign 

In  writing  pounds,  place  the  sign  first;  thus,  £5. 
A  farthing,  like  a  mill,  is  not  coined,  but  is  expressed  as  a  fraction 
of  a  penny. 

French  Money 

The  standard  unit  of  French  money  is  the  f ranc  =  $.193. 

100  centimes  =  1  franc  (fr.). 

The  peseta  of  Spain  and  the  lira  of  Italy  are  of  the  same 
value  as  the  franc.  The  franc  is  the  standard  unit  of  value 
also  in  Belgium  and  Switzerland. 


182  DENOMINATE   NUMBERS 

German  Money 

The  standard  unit  of  German  money  is  the  mark  =  1.238. 

100  pfennigs  (pf.)  =  1  mark  (m.). 

All  systems  of  money,  except  English  money,  are  decimal 
systems.  Canada  has  a  decimal  system  of  money  like  the 
United  States.  The  denominations  are  the  dollar,  the  dime, 
the  cent,  and  the  mill. 

Memorize: 

1  pound      =  $4.8665 

1  franc  =  .193  Approximate  Values 

1  peseta      =193  1  pound=$5.00 

1  lira  =  .193  1  mark  =  .25 

1  drachma  =  .193  1  franc  =  .20 
1  mark       =  .238 

Change: 

1.  £  1  to  8. ;  to  d.  5.    615  centimes  to  francs. 

2.  200  centimes  to  francs.  6.    8.5  m.  to  pfennigs. 

3.  £1  5s.  to  s.  7.    G|  francs  to  centimes. 

4.  5  francs  to  centimes.  8.    15  shillings  to  d. 

9.   A  lady  paid  <6d.  a  yard  for  cloth.     Find  the  cost,  in 
shillings,  of  20  yards. 

10.  An  English  merchant  takes  1  pound  and  5  half  sov- 
ereigns to  a  bank  to  exchange  for  pennies.  How  many 
pennies  does  the  merchant  receive  ? 

11.  The  admission  to  a  German  show  costs  50  pfennigs. 
How  many  tickets  can  be  bought  for  5|  marks? 

12.  In  a  French  school  a  collection  for  charity  contained 
6  francs,  5  half  francs,  and  250  centimes.  Find  the  value 
in  francs. 


FOREIGN    MONET  183 

Written  Work 

Change  to  U.S.  money,  expressed  in  the  nearest  cent: 

1.  £37.5.  5.    575  m. 

2.  675  lira.  6.    380  drachmas. 

3.  579  peseta.  7.    786.8  fr. 

4.  £35.  8.    £6. 

9.    Change  £ 25  12s.  Sd.  to  U.S.  money.     Change  12s.  Sd. 
to  the  decimal   of  a  pound;  thus,  Sd.  =  ^j,  or  |s. ;    12s.  4- 

12| 
20 


f s.  =  12f «.     12§s.  =X4^,  or  £.633+. 


Hence,  £25  12s.  8rf.  =  £25.633. 

1  pound  =  $4.8665. 

25.633  x  $4.8665  =  $124.74. 

Change  to  U.S.  money  expressed  to  the  nearest  cent. 

10.  £10    5s.     6<*.  14.    £87  10s.  Hd. 

11.  £27  lid.  15.    769  lira. 

12.  £98  19s.    bd.  16.    104  fr.  75  centimes. 

13.  100  m.  60  pf.  17.    745  peseta. 

18.  Change  $1685  to  pounds,  etc. 

$1685  -s-  $4.8665  =  346.244+,  the  number  of  pounds. 
.244  x  20s.         =  4.88s. 
.88  x  \2d.        =  10.56rf.  =  to  the  nearest  penny  lid. 
Hence, $  1685  =  £346  4s.  lid. 

19.  The  cost  of  a  bill  of  goods  in  England  was  $  780.50. 
Express  the  value  to  the  nearest  penny  in  English  money. 

20.  A  German  clock   cost  in  Strasburg   $  119.     Express 
the  value  to  the  nearest  pfennig  in  German  money. 

21.  An  Italian  workman  saved  on  an  average  $27.89  per 
month.     Find  the  value  to  the  nearest  lira. 


184  DENOMINATE   NUMBERS 

ADDITION  AND   SUBTRACTION 

In  addition,  subtraction,  multiplication,  and  division  of 
denominate  numbers,  the  work  is  performed  just  as  with 
other  numbers.  It  is  necessary,  however,  to  bear  in  mind 
how  many  units  of  any  denomination  equal  one  unit  of  the 
next  higher  denomination. 


Written  Work 


l.    Add  : 


6  yd.  2  ft.  4  in.  The  sum  of  the  inches  is  18  in.  or  1  ft.  6  in. 

3  2         6  Write  6  in.  and  add  1  ft.  to  the  feet.     The  sum  of 

9         „  the  feet  is  7  ft., or  2  yd.  1  ft.     Write  1  ft.  and  add 

2  yd.  to  the  sum  of  the  yards.  The  sum  of  the 
yards  is  15  yd.     The  sum  is  15  yd.  1  ft.  6  in. 


15        1        6 


2.  Subtract  54  lb.  9  oz.  (av.)  from  75  lb.  4  oz.  (av.). 

.,  9  oz.  cannot  be  subtracted  from  4  oz.     Chauge  75  lb.  4  oz. 

lb.      OZ.       to  7i  lb  20  Qz     2()  oz  _-9  Qz  _  n  oz  ^  whjch  is  written  in 

"5        4        the  remainder.     74  lb.  left  in  the  minuend  -  54  lb.  =  20  lb. 
54        9        Hence,  the  remainder  is  20  lb.  11  oz. 

20     11 

3.  Add  :  4.    Add  : 

bu.  pk.  qt.  hr.  min.  sec. 

16   3  5  18   44  48 

18   0  7  21   39  29 

42   1  0  27  51  58 

56   1  3  29   36  24 


5.  Subtract :  6.  Subtract  : 

hr.  min.  yr.  mo.  wk.  da. 

23   42  21   5   3  4 

17   56  9   7   3  6 


ADDITION   AND  SUBTRACTION  185 

The  most  important  application  of  subtraction  of  denomi- 
nate numbers  is  in  rinding  the  difference  between  two 
dates. 

7.  How  long  a  time  elapsed  from  April  19, 1775  to  April 
14,1861? 

The  later  date  is  written  in  the   minuend   as  the 

yr.    mo.    da.      Uth  day  of  the  4th  month  of  1861 ;  and  the  earlier 

1861      4      14       date  in  the  subtrahend    as  the    19th  day  of  the  4th 

1775      4      10       month  of  1775.     In  borrowing,  consider  30  days  to  a 

— ^FTT — ly7     month  and  12  months  to  a  year.    The  difference  will  be 

the  time  in  years,  months,  and  days. 

8.  Washington  was  born  February  22,  1732  ;  he  was  in- 
augurated president  April  30,  1789.  How  old  was  he  when 
he  became  president  ? 

9.  Find  the  time  from  the  signing  of  the  Declaration  of 
Independence,  July  4,  1776  to  the  beginning  of  the  Civil 
War,  April  14,  1861. 

10.  General  Ulysses  S.  Grant  was  born  April  27,  1822. 
How  old  was  he  when  the  Civil  War  closed  April  9, 
1865? 

11.  Find  the  sum  of  the  collections  at  an  English  theater 
for  four  different  evenings  as  follows  :  £  479  10s.  Sd.  ;  £  531 
15s.  l\d.  ;   £  594  9d.  ;   £  401  lis.  hd. 

12.  Find  the  difference  between  the  largest  collection  in 
problem  11  and  each  of  the  others. 

13.  A  United  States  mail  agent  leaves  New  York  Monday 
on  his  trip  to  Buffalo  at  9:35  a.m.  and  returns  Tuesday  at 
6: 15  p.m.     How  long  is  he  gone? 

14.  A  coal  miner's  4  wagons  for  the  day  weighed  as 
follows  :  1  T.  6  cwt.  19  lb. ;  1  T.  7  cwt,  13  lb. ;  1  T.  5  cwt. 
85  lb.  ;  1  T.  4  cwt.  98  lb.     Find  the  total  weight. 


186  DENOMINATE   NUMBERS 

MULTIPLICATION  AND  DIVISION 

Written  Work 

1.  A  square  field  is  40  rd.  5  yd.  and  2  ft.  on  a  side.  Find 
the  perimeter,  or  the  distance  around  the  field. 

rd.    yd.     ft.  4xo  ft.  _  8  ft.  or  2  yd.  2  ft. 

40        5       2  4x5  yd.  =  20  yd. ;  20  yd.  +  2  yd.=  22  yd.  or  4  rd. 

4  4  x  40  rd.  =  160  rd. ;  160  rd.  +  4  rd.  =  164  rd. 

TgT        n       o  The  perimeter  of  the  field  is  164  rd.  2  ft. 

2.  Six  English  workmen  divide  their  profits  equally.  Find 
each  one's  share,  if  the  total  profits  are  X  44  17s.  6d. 

£     8.     d.         £  44  -  6  =  £  7  and  £  2  remaining  ;    £  2  =  40s. ;  40s. 

6  )44  17     6      +  ^s'  =  ^s" '    *^s'  ^  ^  —  ®s-   and  3s.  remaining  ;  3s.  = 
— „     q     „     36rf. ;    36rf.  +  6(7.  =  42rf.   42rf.  -  6  =  Id.     The  share  of 
each  workman  is  £  7  9s.  Id. 

Division  may  be  performed  by  changing  all  the  denomina- 
tions to  a  common  denomination  ;  thus,  164  rd.  2  ft.  -5-  40  rd. 
5  yd.  2  ft.  =  2708  ft,  -s-  677  ft,  =  4,  the  quotient ;  or  by  ex- 
pressing the  common  denomination  as  a  mixed  decimal  ;  thus, 
172  ft.  3  in.  -s-  6  ft.  6  in.  =  172.25  ft.  -*-  6.5  ft.  =  26.5,  the 
quotient. 

3.  A  gardener  sold  on  an  average  6  bushel  crates  and 
17  baskets  of  blackberries  each  day  for  8  days.  Find  the 
total  number  of  bushels  and  baskets  sold. 

4.  57  students  at  a  ball  game  each  wore  a  badge  5^  inches 
long.  How  many  yards  and  inches  of  ribbon  were  needed  to 
make  the  badges  ? 

5.  A  wire  fence  inclosing  a  square  field  40  rd.  5  yd.  on  a 
side  has  4  wires.     Find  the  total  length  of  wire  in  feet. 

6.  A  45  horse-power  automobile  used  on  an  average  3  gal. 
3  qt,  1  pt.  of  gasoline  daily  on  a  certain  trip  of  11  days. 
Find  the  number  of  gallons,  etc,  used. 


MULTIPLICATION    AND   DIVISION  187 

7.  Aii  English  estate  of  X  8000  10s.  Sd.  was  divided  as 
follows:  the  widow  received  \  of  the  estate  and  the  re- 
mainder was  equally  divided  among  5  children.  Find  the 
amount  to  the  nearest  cent  in  United  States  money  that 
each  received. 

8.  A  Greek  confectioner  bought  12  bushels  of  chestnuts 
at  82.50  per  bushel  and  retailed  them  at  5^  per  pint. 
Find  his  gain. 

9.  How  many  times  will  a  wheel  10  feet  8  inches  in 
circumference  turn  in  going  12  miles  ? 

10.  A  ball  room  is  46|  feet  long  and  30|  feet  wide.  Find 
the  cost  of  a  picture  molding  around  it  at  9  ^  per  foot. 

11.  A  bicyclist  traveled  63  miles  170  rods  2  yards  in  a 
forenoon,  and  30  miles  5Q  rods  less  in  the  afternoon.  Find 
the  distance  he  traveled  that  day. 

12.  A  silver  dollar  weighs  4121  grains.  Find  in  tons,  etc., 
the  weight  of  $5,600,000  silver  dollars. 

13.  A  horse  is  fed  1|  pecks  of  oats  per  day.  How  much 
will  the  oats  for  the  horse  cost  at  40  0  per  bushel  for  Decem- 
ber and  January  ? 

14.  Find  |  of  275  ft.  4  in. ;  f  of  11  lb.  8  oz.  ;  j  of  36  bu. 

3  pk.  4  qt. 

15.  A  dairyman's  sales  for  each  of  4  weeks  were  as  fol- 
lows:  1st  week,  115  gal.  3  qt.  1  pt. ;  2d  week,  105  gal.  3  qt. 
1  pt.  ;  3d  week,  113  gal.  1  qt.  ;  4th  week,  103  gal.  1  qt. 
1  pt.  If  ^  of  the  total  sales  were  uncollectable,  find  the  cash 
amount  of  his  sales  for  the  four  weeks  at  7.]  i  per  quart. 

16.  A  city  weighman  one  morning  recorded  the  weight  of 

4  loads  of  hay  as  follows:  1  T.  5  cwt.  19  lb.;  1  T.  7  cwt. 
29  lb.;  1  T.  98  11). :  1  T.  9  cwt.  3  lb.  Find  the  total  amount 
of  the  sales  at  %\\\  per  ton. 


REVIEW   PROBLEMS 

L.    What  is  the  sum  of  $8.45,  $.55,  I.87J,  $15,055,  and 
.45? 

2.  If  .9  of  a  ton  of  structural  iron  is  worth  $23.40,  how 
much  are  11.75  tons  worth? 

3.  Express  as  a  common  fraction  in  its  lowest  terms 
.15625. 

4.  A  huckster  sold  29|  bushels  of  potatoes  at  $.80  a 
bushel  and  bought  apples  with  the  proceeds  at  $2.36  a  bar- 
rel.    How  many  barrels  of  apples  did  he  receive  ? 

5.  A  carpenter  worked  235|  days  for  $2.75  a  day.  He 
received  $480.75.     How  much  was  still  due  him? 

6.  Divide  .0001  by  .00001,  and  multiply  the  quotient  by 
1000. 

7.  If  shovels  are  worth  $15  a  dozen,  how  many  dozen  can 
be  bought  for  $37.50? 

8.  Find  the  sum  of  85  ones,  85  tenths,  85  hundredths, 
and  85  thousandths. 

9.  The  fastest  long-distance  train  in  the  world  (1906) 
runs  from  New  York  to  Chicago,  a  distance  of  979.52  miles, 
in  18  hours.      Find  the  average  rate  per  hour  that  it  runs. 

10.  The  fastest  English  train  runs  for  8  hours  at  a  speed  of 
50.18  miles  per  hour.     What  distance  does  it  run  ? 

11.  The  regular  fare  from  New  York  to  Chicago  is  $21.50, 
but  on  this  fast  train  a  total  excess  fare  of  $9  is  charged. 
What  is  the  actual  cost  per  mile  to  the  passenger  ? 

188 


REVIEW   PROBLEMS  189 

12.  The  train  in  problem  9  makes  6  stops,  averaging  5 
minutes  each.  At  what  rate  must  the  train  aetually  run  so 
as  to  reach  Chicago  from  New  York  in  18  hours  ? 

13.  A  gallon  of  water  weighs  81  pounds.  Cast  iron  is 
7.08  times  as  heavy  as  water.  How  much  would  a  piece  of 
iron  equal  in  volume  to  3.25  gallons  of  water  weigh  ? 

14.  Gold  is  19.3  times  as  heavy  as  water.  How  much 
would  the  same  volume  of  gold  weigh  ? 

15.  A  bushel  of  shelled  corn  weighs  56  pounds.  How 
many  bushels  are  required  to  fill  an  ordinary  freight  car 
whose  capacity  is  60000  pounds? 

16.  The  freight  on  such  a  car  shipped  from  Kansas  City 
to  Albany,  N.Y.,  was  $75.  How  much  was  that  per 
bushel  ? 

17.  This  corn  cost  56  $  per  bushel  in  Kansas  City.  How 
much  did  this  car  load  of  corn  cost  delivered  at  Albany? 

18.  The  dealer's  other  expenses  in  handling  this  car  of 
corn  were  127.50.  He  sold  it  for  70  cents  per  bushel.  How 
much  did  he  gain  ? 

19.  In  an  automobile  race  297  miles  were  covered  in 
290.173  minutes.     What  was  the  time  per  mile? 

20.  The  speed  of  one  machine  in  this  race  was  67.63  miles 
per  hour.  At  this  rate  how  far  could  the  machine  travel  in 
1.25  hours  ? 

21.  How  many  rods  of  hedge  surround  a  school  ground 
8.625  rods  long  and  5.75  rods  wide? 

22.  If  .76  of  a  pound  of  gunpowder  is  niter,  1425.76 
pounds  of  niter  is  necessary  in  making  how  many  pounds  of 
gunpowder? 

23.  \  -  (.125  x  7)  +  (16  x  .375)  =  ? 


190  REVIEW   PROBLEMS 

24.  If  the  price  of  gas  is  1.27  per  thousand  cubic  feet, 
how  much  is  the  average  gas  bill  per  month,  when  85620 
cubic  feet  are  consumed  in  6  months? 

25.  Allowing  2.75  bushels  to  the  barrel,  how  many  barrels 
of  apples,  at  $.65  a  bushel,  can  be  bought  for  $178.75? 

26.  A  teacher  paid  .35  of  his  salary  for  board,  .18  for 
clothing,  .07  for  travel,  .1  for  incidentals,  and  had  $300  left. 
How  much  was  his  salary? 

27.  From  3|  take  the  sum  of  3|  thousandths  and  3|  mil- 
lionths. 

28.  If  seventy-five  hundredths  of  a  number  is  372,  what 
is  eighty-three  and  one  third  hundredths  of  it? 

29.  What  is  the  value  of  (~  ~  ^?  +  -)  x  -03? 

V.4       4.5      2/ 

30.  A  real  estate  agent  bought  4  lots  at  $650.50  each. 
He  sold  two  of  them  at  a  loss  of  $67.25.  If  he  sells  the  other 
two  at  a  profit  of  $75.75,  how  much  does  he  gain  on  his 
investment  ? 

31.  A  school  board  paid  $144  for  books :  §  of  the  amount 
was  paid  for  General  Histories  at  $1.20  each;  ^  of  it  for 
Algebras  at  $1  each  ;  and  the  remainder  for  Rhetorics  at  $.96 
each.     How  many  books  were  purchased? 

32.  A  man  invested  .32  of  his  money  in  mining  stock,  .48 
in  railroad  stock,  and  had  $12000  remaining.  How  much 
had  he  at  first? 

33.  An  engineer  took  a  contract  to  build  a  bridge  for 
$18500.  The  material  cost  $10575;  he  employed  40  men 
7^  weeks  of  six  days  each  at  $2.25  per  day,  and  30  men  for 
41  weeks  of  five  days  each  at  $2.75  a  day.  How  much  did 
he  gain? 


REVTEW   PROBLEMS  191 

34.  A  merchant  bought  140  boys'  suits  at  $6.75  a  suit. 
He  sold  |  of  them  at  19.50  a  suit  and  the  remainder  at 
$8.50  a  suit.     How  much  did  he  gain? 

35.  Four  men  purchased  an  oil  property,  the  first  paying 
for  .3  of  it,  the  second  for  .375  of  it,  the  third  for  |  of  it, 
and  the  fourth  the  remainder,  which  was  $3000.  How 
much  did  the  property  cost  them  ? 

36.  A  merchant  bought  975  pounds  of  sugar  for  $48.75. 
He  sold  |  of  it  at  $.055  a  pound,  £  of  it  at  $.06  a  pound,  and 
the  remainder  at  $.065  a  pound.     Find  his  gain. 

37.  I  invested  .4  of  my  money  in  a  farm  and  deposited  .75 
of  the  remainder  in  a  bank.  If  the  amount  paid  for  the 
farm  was  $300  less  than  the  amount  deposited  in  the  bank, 
how  much  money  had  I? 

Find  the  sum  of  the  quotients : 
38. 


40. 


5  + 

5 

39.      .6  + 

.2 

5  + 

.5 

66- 

.22 

5  + 

.05 

11- 

.022 

5  + 

.005 

.08  + 

.2 

.005  + 

5 

.088  + 

22 

.5-5- 

5 

.16  + 

.004 

500  + 

.5 

.078  + 

.013 

001 +.01 

41. 

3.24  +  18 

42.  .002  +  20 

.72-5-.  004 

.5+.  0125 

81.11  +  6.1 

096 -5-.  32 

675 +  .75 

.003  +  37.5 

198-6.6 

9  +  .225 

16  +  . 016 

.05-=-. 125 

.288  +  32 

.4+250 

8.1 +  .09 

100 +  .001 

40.04  +  1.43 

216 -.036 

39. 2 +  .14 

.576  +  . 8 

.8-160 

4.4  +  55 

43.3  +  100 

PRACTICAL   MEASUREMENTS 

LENGTH  AND  SURFACE 

To  the  Teacher.  —  Secure  a  50-foot  tape  measure  and  have  pupils 
make  as  many  actual  measurements  as  possible. 

1.  Find  the  dimensions  of  the  school  ground. 

2.  If  your  school  is  in  the  city,  measure  the  length  and 
width  of  some  square  near  your  school,  or  if  in  the  country, 
some  field. 

3.  Measure  |  of  a  mile  along  a  street  or  a  public  road. 

Compare  a  mile  with  a  rod ;   with  a  yard  ;  with  a  foot. 

After  some  practice  in  actual  measurements,  the  pupils  should  be  able 
to  give  quite  accurate  estimates  of  short  distances. 

4.  Have  the  pupils  estimate  the  length  and  the  height  of 
the  schoolroom  ;  the  height  of  the  school  building;  the  length 
and  the  width  of  the  playground,  etc. 

5.  Have  each  pupil  draw  on  the  blackboard,  without 
the  aid  of  a  rule,  an  inch,  a  foot,  a  yard. 

6.  Show  by  diagram  the  number  of  square  inches  in  a 
square  foot. 

7.  Show  by  diagram  the  number  of  square  feet  in  a 
square  yard. 

8.  Draw  a  square  rod  on  a  scale  of  3  inches  to  1  yard. 

9.  Show  by  a  diagram,  on  a  scale  of  1  inch  to  the  yard, 
the  number  of  square  yards  or  square  feet  in  a  square  rod. 

160  square  rods  of  land  is  called  an  acre. 
A  square  mile  of  land  is  called  a  section  of  land. 

192 


LENGTH   AND   SURFACE  193 

10.  How  many  yards  are  there  in  the  perimeter  of  a  field 
a  mile  square  ? 

Note. The  perimeter  of  a  figure  is  the  line  that  bounds  it,  or  the 

sum  of  its  sides. 

11.  Name  the  different  units  of  long  measure  and  the 
different  units  of  surface  measure. 

12.  What  is  the  shape  of  the  figure  that  represents  a  square 
inch  ?  a  square  foot  ?  a  square  yard  ?  a  square  rod  ? 

13.'  Draw  two  figures  of  different  dimensions  to  represent 
an  acre.  How  do  you  show  that  160  square  rods  equals 
each  surface? 

14.  What  unit  of  surface  measure  is  not  a  square  unit? 

15.  Have  each  pupil  draw  a  unit  surface,  without  the  aid 
of  a  rule,  to  show  a  square  inch,  a  square  foot,  a  square  yard. 

Learn  this  table  of  surface  or  square  measure : 


144  square  inches  (sq.  in.)     =1  square  foot 
9  square  feet  (sq.  ft.)  =  1  square  yard  (sq.  yd.) 

304  S(luare  yards  fa-  yd0  }  =  1  square  rod  (sq.  rd.) 
272 \  square  feet  (sq.  ft.)      j 

160  square  rods  (sq.  rd.)       \  =\  acre  (A ) 
43560  square  feet  (sq.  ft.)       j 

1  mile  square  =  1  section 

640  acres  =  1  square  mile 

36  square  miles  =  1  western  township 

100  square  feet  =1  square  in  roofing  and  flooring 


Written  Work 
Change : 

1.  3  sq.  ft.  48  sq.  in.  to  square  inches. 

2.  4  A.  35  sq.  rd.  to  square  rods. 

3.  125  sq.  rd.  to  a  decimal  of  an  acre. 

4.  .375  of  an  acre  to  square  rods. 

HAM.    COMPL.    A  l;  1  111.  —  18 


194  PRACTICAL  MEASUREMENTS 

5.  4  A.  to  square  feet. 

6.  |  sq.  ft.  to  square  inches. 

7.  4.5  sq.  rd.  to  square  inches. 

8.  1\  sq.  mi.  to  square  rods. 

9.  1800  sq.  rd.  to  acres,  etc. 

10.  1584  sq.  in.  to  square  feet,  etc. 

11.  6.75  A.  to  square  feet. 

12.  Mr.  Jamison's  farm  contains  125  A.  120.8  sq.  rd. 
Three  fourths  of  it  is  purchased  at  $312.50  per  acre,  to  be 
laid  out  in  town  lots.  Find  the  number  of  acres  sold  and 
the  amount  received  from  the  sale. 

LINES  AND  ANGLES 

1.  Observe  the  two  lines.     How  do  they      

compare  in  direction  ? 

Parallel  lines  are  lines  that  cannot  meet  however  far  they 
may  be  extended. 

An  angle  is  the  difference  in  direction  of  two  lines  that  meet. 

When  two  lines  meet  each  other  forming  a  square  corner, 
they  form  a  right  angle ;  thus,    | 

Lines  drawn  at  right  angles  to  each  other  are      . 

perpendicular  ;     thus,  AB  and  BD   in    the  cut  are      | 

perpendicular  to  each  other.  B 

2.  Draw  a  circle  and  divide  it  into  4  equal  parts  by 
diameters  perpendicular  to  each  other. 

3.  How  many  angles  are  there  at  the  center 
of   the   circle  ?      What  is  each   angle  called  ? 

The  circumference  of  a  circle  is  the  perimeter 
or  distance  around  it.  The  circumference  of  a 
circle  is  measured  in  degrees;   every  circum- 


LINES   AND   ANGLES 


195 


ference,  whether  large  or  small,  is  divided  into  360  degrees 
(written  360°;. 

}  of  a  circle  is  90°.  Observe  that  the  angle  between 
two  lines  that  meet  at  a  point  is  measured  l>y  the  part 
of  the  circumference  cut  by  the  lines  extended. 

4.  How  do  you  explain  that  ^  of  circum- 
ference A  contains  as  many  degrees  as  ^  of 
circumference  B? 

5.  Observe  the  figure.  Show 
that  the  curved  lines  are  simply 
parts  of  circumferences  of  circles  B 
that  could  be  formed  about  the 
point  B.  How  do  you  show  that 
each  curved  line  measures  an  angle  of  30°  ? 
gles  on  the  figure. 


Show  the  an- 


6.  Show  that  an  angle  is  the  difference  in  direction  of  two 
lines  that  meet  at  a  point  and  that  the  angle  remains  the 
same,  however  far  the  lines  may  be  extended. 


Angular  Measure 

Angles  are  measured  by  an  instrument  called  a  protractor. 

When  the  center  0  of  the 
protractor  is  placed  at  the 
vertex  of  the  angle  to  be 
measured,  the  size  of  the 
angle  may  be  seen  on  the 

scale  between  the  lines  that     A  0  B 

form  the  angle.     Thus,  BOO  is  an  angle  of  30°,  and  AOC  is 
an  angle  of  150°. 

Every  circumference  contains  360    degrees  (360°),  each 
degree,  60  minutes  (60'),  and  each  minute,  60  seconds  (60"). 


196 


PRACTICAL   MEASUREMENTS 


Table  of  Angular  Measure 


60  seconds  (' 
60  minutes 
360  degrees 

')  =  1  minute  (') 
=  1  degree  (°) 
=  1  circumference  (C) 

The  length  of  a  degree  at  the  equator  is  691  miles. 
Draw  an  angle  of  90°;  45°;  60°;   120°;  30°. 

Kinds  of  Angles 


Which  one  of  these  angles  is  a  right  angle  ?  Why  ? 
Which  is  less  than  a  right  angle  ?  Which  is  greater  than 
a  right  angle? 

A  right  angle  is  an  angle  of  90°. 

An  acute  angle  is  an  angle  less  than  90°. 

An  obtuse  angle  is  an  angle  greater  than  90°. 


TRIANGLES 

A  triangle  is  a  surface  bounded  by  three  straight  lines. 
(Tri  means  three.^) 

A  vertex  of  a  triangle  is  a  point  where  two  sides  meet. 

The  base  of  a  triangle  is  the  side  on  which  it  seems  to 
rest. 

The  altitude  of  a  triangle  is  the  perpendicular  distance 
from  the  vertex  opposite  the  base  to  the  base,  or  the  base 
extended. 


T  III  AN(1  LESS 


197 


Triangles  are  named  in  two  ways : 
I.    From  their  angles  : 

(1)  Right-angled  triangles.      (One  right  angle.) 

(2)  Acute-angled  triangles.     (All  angles  less   than  a 

right  angle.) 

(3)  Obtuse-angled  triangles.     (One  angle  greater  than 

a  right  angle.) 


Right-angled 


Acute- angled 


Obtuse- angled 


II.    From  their  sides  : 

(1)  Equilateral.      (Having  three  sides  equal.) 

(2)  Isosceles.      (Having  two  sides  equal.) 

(3)  Scalene.     (Having  no  two  sides  equal.) 


Equilateral 


Isosceles 


Scalene 


Measuring  degrees  and  angles. 

1.  How  many  right  angles  are  there  in  the 
square  ? 

2.  How  many  right  angles  are  there  in  the 
rectangle  ? 

3.  Cut  from  paper  a  square.  Fold  it  on 
the  line  connecting  the  opposite  corners,  and 
cut  it  into  two  triangles. 


Square 


Rectangle 


4.    How    many  degrees    are  there  in  each  angle  of    each 


triangle  thus  formed? 


198 


PRACTICAL  MEASUREMENTS 


5.    Every  right  triangle  contains  how  many  degrees? 

By  Geometry  it  is  shown  that  the  sum  of  the  angles  in  any 
triangle  is  equal  to  180°.  This  can  also  be  shown  by  meas- 
uring the  angles  with  a  protractor. 

The  sum  of  all  the  angles  of  any  triangle  is  equal  to  two  right 
angles,  or  180°. 

The  following  numbers  in  each  case  represent  the  size  of 
two  angles  of  a  triangle.     Find  the  size  of  the  third  angle : 


6.    90°  and  45° 

10.    60°  and  40° 

7.    90°  and  60° 

11.    100°  45'  and  37° 

8.    120°  and  30° 

12.    75°  10'  and  95°  30' 

9.    1201°  and  601° 

13.    100°  and  45°  40' 

KEOIAJSULli 


QUADRILATERALS 

A  quadrilateral  is  a  surface  having  four  straight  sides. 
(Quadrilateral  means  having  four  sides. ) 

l.  Examine  the  quad- 
rilaterals. What  are  the 
essential  features  of  A  ? 

A  square  is  a  quadri- 
lateral having  four  equal 
sides  and  four  right  angles. 

2.  What  are  the  essential  features  of  B  ?     In  what  way 
does  figure  B  differ  from  figure  A  ? 

A  rectangle  is  a  quadrilateral  having  four  straight  sides 
and  four  right  angles. 

3.  Show  that  the  opposite  sides  of  a  rectangle  must  be 
equal  and  parallel.     Is  a  square  a  rectangle  ? 

A  parallelogram  is  a  quadrilateral  whose  opposite  sides  are 
parallel. 


Square 


AREAS  OK   RECTANGLES 


199 


D 


liaoimoiu 


4.  Examine    these    quadrilat- 
erals.     Why  are  they  parallelo- 
grams ?      How    do    the    sides  of 
surface    C  compare    in    length  ?    **°**™ 
Show  that  its  angles  are  not  right  angles. 

A  rhombus  is  a  quadrilateral  whose  sides  are  equal,  and 
whose  angles  are  not  right  angles. 

5.  Why  is  surface  D  a  parallelogram  ?       Show  that  its 
angles  are  not  light  angles.    Show  that  its  sides  are  not  equal. 

A  rhomboid  is  a  quadrilateral  whose  opposite  sides  are  equal 
and  whose  angles  are  not  right  angles. 

6.  Why  is  surface  E 
a  quadrilateral  ?  Why 
is  it  not  a  parallelo- 
gram?    How   many   of 


TBAI'EZOID 


Tkatezium 


its  sides  are  parallel  ? 

A  trapezoid  is  a  quadrilateral  having  but  two  sides  parallel. 

7.  Why  is  surface  F  not  a  trapezoid  ?     What  is  its  name  ? 
A  trapezium  is  a  quadrilateral  having  no  two  sides  parallel. 

8.  Describe  each  of  the  six  quadrilaterals  named  above 
with  reference  to  its  sides  and  angles.  How  many  of  these 
quadrilaterals  are  parallelograms  ?     Give  reasons. 


AREAS   OF   RECTANGLES 


Finding  the  area  of  a  rectangle. 

Find  the  area  of  a  rectangle  4  yd. 
long  and  3  yd.  wide.  How  long  is  this 
rectangle  ?  how  wide  ?  What  is 
the  unit  of  measure  ?  How  many 
such  units  are  in  the  first  row?  in 
the  second  ?  in  the  entire  surface  ? 


4yd. 


*fsq. 

yd 

200  PRACTICAL  MEASUREMENTS 

If  the  length  and  width  of  a  rectangle  are  expressed  in  inches,  the 
unit  of  measure  is  1  sq.  in.;  if  expressed  in  feet,  the  unit  of  measure  is 
1  sq.  ft. ;  if  expressed  in  rods,  the  unit  of  measure  is  1  sq.  rd.  If  the  length 
and  width  are  expressed  in  related  units,  as  feet  and  inches,  or  yards, 
feet,  etc.,  the  dimensions  must  be  changed  to  like  units  before  finding 
the  area,  that  is  the  number  of  square  units  it  contains. 

Written  Work 

1.  Find  the  area  of  a  flower  bed  20  feet  8  inches  in  length 

by  10  feet  6  inches  in  width. 

Length  =  20§  ft. ;  width   =  10|  ft. 
Area      =  20§  x  10£  x  1  sq.  ft.,  or 
-632  x  ^  x  1  sq.  ft.  =  217  sq.  ft. 

Tlie  area  of  a  rectangle  is  found  by  multiplying  its  unit  of 
measure  by  the  product  of  its  two  dimensions  when  expressed  in 
like  units. 

Find  the  areas  of  rectangles  having  the  following  dimen- 
sions : 

2.  20.5  ft.  by  12  ft.  6.  115  ft.  by  54  in. 

3.  21  ft.  by  6.9  ft.  7.  45  yd.  by  7  ft. 

4.  72  yd.  by  401  yd.  8.  108  in.  by  3  ft. 

5.  6  yd.  1  ft.  by  3  yd.  2|  ft.        9.  54  ft.  by  108  in. 

10.  How  many  square  yards  are  there  in  a  lawn  45  feet 
long  and  36  feet  wide  ? 

11.  A  square  ball-park  600  feet  on  a  side  is  inclosed  with 
a  tight  board  fence  9  feet  in  height.  Find  the  outside  sur- 
face of  the  fence  in  square  yards. 

12.  Compare  in  area  a  surface  8  inches  square  and  a  sur- 
face 2  inches  square  ;  a  surface  20  rods  square  and  a  surface 
40  rods  square. 

13.  Bricks  are  generally  8  in.  x4  in.  x  2  in.  in  size.  Esti- 
mate the  number  necessary  to  lay  a  sidewalk  100  ft.  long 
and  5  ft.  wide,  if  the  bricks  are  laid  on  the  flat  side.  Find 
the  cost  of  the  bricks  needed  at  $13.75  per  thousand. 


PLASTERING   AND   TAINTING  201 

14.  A  surveyor  finds  a  field  in  the  form  of  a  rectangle  to 
be  680  ft.  long  and  330  ft.  wide.  Find  its  area  without 
changing  feet  to  rods. 

15.  A  field  in  the  form  of  a  rectangle  contains  1200  sq.  rd. 
and  the  length  is  40  rods.      Find  the  width. 

16.  How  many  lots,  each  30  ft.  by  120  ft.,  can  be  made 
from  a  plot  of  ground  120  ft.  in  depth  and  containing 
10800  sq.  ft.  ?     (Make  a  diagram.) 

PLASTERING  AND  PAINTING 

In  plastering,  painting,  and  kalsomining,  the  unit  of  meas- 
ure is  the  square  yard. 

In  some  localities  an  allowance  is  made  for  openings  and  baseboards, 
but  there  is  no  uniform  rule  in  practice.  Any  allowance  should  always 
be  specified  in  the  contract. 

There  are  either  50  or  100  laths  in  a  bundle.  A  bundle 
of  100  is  generally  estimated  to  cover  5  square  yards  of 
surface. 

Written  Work 

1.  How  many  square  yards  of  plaster  are  necessary  to 
cover  the  ceiling  of  your  classroom  ? 

2.  Find  the  cost  of  painting  both  sides  of  a  tight  board 
fence,  150  ft.  long  and  8  ft.  high,  at  15  ^  per  square  yard. 

3.  Allowing  nothing  for  openings,  how  much  will  it  cost 
to  kalsomine  the  walls  and  ceiling  of  a  room  20  ft.  long, 
16  ft.  wide,  and  12  ft.  high,  at  6^  per  square  yard  ? 

4.  A  store  room  is  75  ft.  long,  20  ft.  wide,  and  15  ft. 
from  floor  to  ceiling.  It  has  a  door  in  the  rear  7  ft.  by 
3£  ft.,  and  a  window  8  ft.  by  3  ft.  How  many  bundles  of 
laths,  each  containing  100,  are  required  for  the  sides,  rear, 
and  ceiling,  making  full  allowance  for  openings  ? 


202 


PRACTICAL   MEASUREMENTS 


5.  How  much  will  it  cost  to  plaster  the  walls  and  ceiling 
of  a  store  room,  40  ft.  by  18  ft.  and  12  ft.  high,  at  6^  per 
square  yard  for  lathing,  and  18^  per  square  yard  for  plas- 
tering, deducting  ^  the  area  of  2  doors,  each  9  ft.  by  4  ft., 
and  of  4  windows,  each  6^  ft.  by  3|  ft.  ? 

6.  A  building  90  ft.  by  24  ft.  contains  3  stories,  each 
13  ft.  high.  The  first  story  is  plastered  on  the  sides  and 
rear.  The  second  and  third  stories  each  have  3  windows 
in  the  front,  each  8  ft.  by  3^-  ft.,  and  each  2  windows  in  the 
rear,  each  8  ft.  by  3  ft.  If  the  ceilings  are  sheet  iron,  find 
the  cost  of  the  plastering,  at  33^  per  square  yard,  deducting 
for  all  openings. 

7.  In  modern  business  buildings  metal  laths  are  used. 
Estimate  the  cost  of  metal  laths,  for  the  building  in  example 
6,  at  25^  per  square  yard. 

ROOFING  AND  FLOORING 

In  roofing,  tiling,  and  flooring,  the  unit  of  measure  is  the 
square  of  100  square  feet. 


Written  Work 

1.  Each  of  the  two  slopes  of  a  roof  is  60  ft.  long  and  20  ft. 
wide.  Find  the  cost  of  covering  them  with  tar  paper  at 
•$5.60  per  square. 

2.  The  floor  of  a  hallway  30  ft.  by  12  ft.  is  inlaid  with 
2-inch  square  tile.     Find  the  number  necessary. 

In  roofing  with  slate, 
each  course  of  slate  is  part- 
ly overlapped.  Each  slate 
as  here  shown  is  10  in.  by 
16  in.  and  has  4  in.  ex- 
posed to  the  weather. 


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ROOFING    AND   FLOORING  203 

3.  How  many  square  inches  of  each  slate  are  exposed? 

4.  If  a  10-inch  by  16-inch  slate  is  exposed  4  inches  to  the 
weather,  find  the  number  of  slates  necessary  to  lay  a  square 
(10  ft.  by  10  ft.)- 

5.  If  slate  10  in.  by  16  in.  is  laid  6  in.  to  the  weather,  find 
the  number  necessary  to  lay  a  square.  Find  the  weight  of  a 
square  of  slate  at  4;]-  lb.  per  square  foot. 

6.  Each  slope  of  a  roof  is  40  ft.  by  20  ft.  Find  the 
number  of  slates,  10  in.  by  16  in.,  exposed  4  in.  to  the  weather, 
required  for  this  roof,  allowing  nothing  for  breakage.  Find 
the  cost  of  the  slates  at  $5.50  per  square. 

There  are  250  shingles  in  a  bunch. 

Shingles  average  16  inches  in  length  and  4  inches  in  width. 
The  exposed  surface  of  a  shingle  laid  4|  inches  to  the  weather 
is,  therefore,  18  square  inches.  Without  waste  8  shingles 
will  lay  one  square  foot,  and  800  shingles  will  lay  100  square 
feet,  or  1  square.  Allowing  for  waste,  4  bunches,  or  1000 
shingles  are  estimated  to  lay  a  square. 

7.  Allowing  nothing  for  waste,  how  many  bunches  of 
shingles  are  required  to  cover  a  barn  roof  35  ft.  in  width  on 
each  side  and  70  ft.  in  length.  Find  the  cost  at  $4.00  per 
thousand  shingles. 

8.  Adding  \  for  waste,  estimate  the  cost  at  $3.50  per 
thousand  of  157  bunches  of  shingles  required  to  cover  the 
roof  in  example  7. 

Flooring  is  frequently  estimated  by  the  square. 

9.  How  much  will  it  cost,  at  $5.00  per  square,  to  lay  the 
floor  of  a  hall  30  ft.  by  60  ft.,  adding  l  for  waste? 

10.  Estimate  the  number  of  squares  of  flooring  required 
for  two  floors  of  a  store  room  25  ft.  by  60  ft. 


204  PRACTICAL   MEASUREMENTS 

PAPERING   AND   CARPETING 

The  unit  of  measure  in  wall  paper  is  the  single  roll,  which 
is  8  yards  in  length  and  usually  18  inches  in  width.  A  double 
roll  is  16  yards  in  length. 

In  approximating  the  number  of  rolls,  paper  hangers  generally  deduct 
from  the  perimeter  of  the  room  the  width  of  the  doors  and  windows. 
The  remaining  number  of  feet  divided  by  H  ft.  (18  in.  =  1|  ft.)  gives  the 
number  of  strips  required  for  the  surface  of  the  wall.  Dividing  the 
total  number  of  strips  by  the  number  that  can  be  cut  from  a  double 
roll  gives  the  number  of  double  rolls  required.  Fractional  parts  of  a  roll 
are  not  sold.  The  ends  of  the  rolls  are  generally  sufficient  to  paper  the 
surfaces  above  and  below  the  doors  and  windows.  Border  is  sold  by  the 
linear  yard. 

Carpet,  matting,  and  border  are  sold  by  the  linear  yard. 
Oil  cloth  and  linoleum  are  sold  by  the  linear  yard  or  by  the 
square  yard.  Ingrain  carpets  are  usually  1  yard  wide,  other 
carpets  are  generally  27  inches  wide. 

Liberal  allowance  must  be  made  for  loss  in  matching. 

Written  Work 

1.  Estimate  the  number  of  double  rolls  of  paper  required 
for  a  ceiling  18  ft.  by  22  ft.,  strips  running  lengthwise. 

22  ft.  =  length  of  one  strip. 
16  yd.  =  48  ft. ;  48  ft.  -4-22  ft.  =  2,  the  number  of  whole  strips  in  a 

double  roll. 
18  ft.  -4-  li  ft.  =  12,  the  number  of  strips  required. 

12  -=-  2  =  6,  the  number  of  double  rolls  required. 

2.  A  dining  room  15  ft.  by  22  ft.  is  11  ft.  from  baseboard 
to  ceiling.  It  has  four  openings  3^  ft.  by  7  ft.  Estimate 
the  paper  required  for  it,  strips  on  ceiling  running  lengthwise. 

3.  The  dining  room  in  problem  2  lias  a  plate  rail  extend- 
ing around  it  between  the  openings.  Find  the  cost  of  this 
rail  at  80^  per  foot. 


PAPERING   AND  CARPETING  205 

4.  How  much  carpet  27  in.  wide,  laid  the  long  way  of  the 
room,  is  required  for  a  room  18  ft.  long  and  15  ft.  wide, 
allowing  12  in.  on  each  strip  except  the  fust  for  matching  ? 

6  yd.  =  the  length  of  one  strip. 

27  in.  =  2\  ft. ;  and  15  ft.  ■*-  2\  ft.  =  %  therefore 

7  =  the  number  of  strips. 
7x6  yd.  =  42  yd. 

6  x  12  in.  =  72  in.,  or  2  yd.,  the  waste  on  6  strip.'-. 
42  yd.  +    2  yd.  =  44  yd.  of  carpet  required. 

5.  Explain  why  it  takes  fewer  yards  of  carpet  to  cover  a 
room  18  ft.  by  27  ft.  with  ingrain  carpet  (1  yard  wide) 
than  with  Brussels  carpet  (27  inches  wide).  Laying  the 
carpet  the  long  way  of  the  room,  how  many  yards  of  each 
would  it  take,  if  10  in.  were  allowed  on  each  strip,  except 
the  first,  for  matching? 

6.  The  widths  of  certain  floors  are  15  ft.,  13^  ft.,  15|  ft., 
18  ft.,  16  ft,  Estimate  the  number  of  strips  of  ingrain  carpet 
necessary  to  cover  each  room. 

7.  Estimate  the  number  of  strips  of  Brussels  carpet 
necessary  to  cover  each  room  described  in  example  6. 

8.  Find  the  cost  of  covering  a  kitchen  13|  ft,  by  12  ft. 
with  linoleum  at  $1.60  per  yard  double  width,  if  £  of  a 
yard  is  allowed  for  matching  and  the  linoleum  is  laid  the 
long  way  of  the  room. 

9.  Estimate  the  difference  in  cost  between  covering  a  room 
18  ft.  by  20^  ft,  with  Axminster  carpet  27  inches  wide, 
at  $1.45  per  yard,  laid  lengthwise,  allowing  12  inches  on 
each  strip  except  the  first  for  matching,  and  covering  the 
room  with  ingrain  carpet  at  85^  per  yard,  laid  in  the  same 
way,  allowing  12  inches  on  each  strip,  except  the  first,  for 
matching. 


206 


PRACTICAL   MEASUREMENTS 


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AREAS 
Finding  the  area  of  a  right  triangle. 

1.    Find  the  area  of  a  right  triangle  whose  base  is  4  yards 
and  whose  altitude  is  3  yards. 

4yd. 

Observe :    1.    That  the  diagonal  divides 

the  rectangle  into  two  equal  right  triangles. 

2.  That  the  unit  of  measure  is  1  sq.  yd. 

3.  That  the  area  of  one  of  the  right  tri- 
angles is  \  of  the  area  of  the  rectangle ;  that 

is,  A  of  4  x  3  x  1  sq.  yd.,  or  6  sq.  yd. 
DdSe 

The  area   of   a  right  triangle  is  found  by  multiplying  the 
unit  of  measure  by  half  the  product  of  the  base  and  the  altitude. 

Name  the  unit  of  measure,  and  find  the  area  of  each  of 
the  following  right  triangles  : 

5.  Base  10  ft.,  altitude  7  ft. 

6.  Base  14  ft.,  altitude  10  ft. 

7.  Base    6  ft.,  altitude  20  ft. 

Finding  the  area  of  any  triangle. 


2.  Base  10  in.,  altitude  6  in. 

3.  Base  12  yd.,  altitude  8  yd 

4.  Base    9  ft.,  altitude  6  ft. 


Written  Work 

1.    Find  the  area  of  two  right  triangles,  the  base  of  one 
being  2  ft.  and  of  the  other  4  ft.  and  the  alt.  of  each  3  ft. 

Draw  the  triangles    as   shown   in   the 
figure. 

Observe  :  1.  That  the  unit  of  measure  is 

1  sq.ft. 

2.  That  the  area  of  the  right  triangle  N 

4  ft.  is  equal  to  \  of  2  x  3  x  1  sq.  ft.,  or  3  sq.  ft. 

3.  That  the   area  of   the  right  triangle  M   is  equal    to   \  of  4  x  3 

x  1  sq.  ft.,  or  6  sq.  ft.     Therefore,  the  area  of  N  plus  the  area  of  M  is 

equal  to  \  of  6  X  3  x  1  sq.ft.,  or  9  sq.  ft. 


AREAS 


207 


2.  Find  the  area  of  a  triangle  whose  base  is  6  ft.  and 
whose  altitude  is  3  ft. 

Observe  that  the  area  of  the  trian- 
gle in  example  2  is  equal  to  the  area  of 
the  two  right  triangles  in  example  1,  and 
is,  therefore,  equal  to  \  of  6  x  3  x  1  sq.  ft., 
or  9  sq.  ft. 

Show  by  cutting  and  folding  paper,  as  indicated  in  the  following 
figures,  that  the  area  of  each  triangle  is  equal  to  one  half  the  area  of 
a  rectangle,  having  the  same  base  and  altitude. 


The  area  of  any  triangle  is  found  by  multiplying  the  unit 
of  measure  by  one  half  the  product  of  the  base  and  altitude. 

Find  the  area  of  the  following  triangles :' 

3.  Base  20  ft.,  altitude  14  ft.     5.  Base  10  ft.,  altitude  30  ft. 

4.  Altitude  8  ft.,  base  15  ft.     6.   Altitude  50  ft.,  base  18  ft. 

Finding  the  area  of  a  parallelogram. 

Find    the   area   of   a   parallelogram  whose  base  is  8  in. 
and  altitude  3  in. 

Observe:  1.  That  the  diagonal  of  the  paral- 
lelogram divides  it  into  two  equal  triangles. 

2.  That  the  area  of  each  triangle  is  equal  to 
\  of  8x3x1  sq.  in.,  and  the  area  of  the 
parallelogram  is  equal  to  |,  or  once  the  prod- 
uct of  the  base  and  altitude ;  that  is,  8  x  3  x  1  sq.  in.,  or  24  sq.  in. 

The  area  of  a  parallelogram  is  found  by  multiplying  the  unit 
of  measure  by  the  product  of  the  base  and  altitude. 


din. 


208  PRACTICAL   MEASUREMENTS 

Written  Work 
Find  the  area  in  acres  of: 

1.  A  parallelogram  whose  base  is  140  rd.  and  altitude  60  rd. 

2.  A  rhomboid  whose  base  is  90  rods  and  altitude  50|  rods. 

3.  A  rhombus  whose  base  is  120  rods  and  altitude  100  rods. 
Find  the  altitude  of  : 

4.  A  rhomboid  whose  area  is  7.5  A.,  base  48  rd. 

5.  A  rhomboid  whose  area  is  6.125  A.,  base  140  rd. 

6.  Find  the  base  of  a  parallelogram  whose  altitude  is  60| 
rods  and  whose  area  is  30.25  acres. 

Finding  the  area  of  a  trapezoid.  • 

Written  Work 

1.    Find  the  area  of  a  trapezoid  whose  parallel  sides  are  20 
inches  and  12  inches,  and  whose  altitude  is  8  inches. 

Examine    the    trapezoid    ABCD.      Draw   the 
-—IHl-^C        diagonal  A  C,  dividing  it  into  two  triangles. 

,--'c;i\  Observe:  1.    That  the  area  of  the  trapezoid  is 

CO;    \      equal  to  the  area  of  its  two  triangles  ABC  and 

2Qm  " Ba  CD. 

2.    That  the  area  of  triangle  ABC  equals  \  of 

20  x  8  x  1  sq.  in. 

3.  That  the  area  of  the  triangle  A  CD  equals  I  of  12  x  8  x  1  sq.  in. 

4.  That  the  area  of  the  trapezoid  equals  |  of  (20+  12)  x  8  x  1  sq.  in.,  or 
128  square  inches. 

The  area  of  a  trapezoid  is  found  hy  multiplying  the  unit  of 
measure  by  the  product  of  the  altitude  arid  ^  the  sum  of  the 
parallel  sides. 

2.  The  parallel  sides  of  a  trapezoid  are  38  inches  and  62 
inches  respectively,  and  its  altitude  is  21  inches  Find  its 
area. 


AREAS 


209 


3.  The  area  of  a  trapezoid  is  2.5  acres.     The  sum  of  it.s 
parallel  sides  is  80  rods.     Find  its  altitude. 

4.  The  area  of  a  trapezoid  is  4±  A.      If  its  altitude  is  20 
rd.,  and  one  of  its  parallel  sides  38  rd.,  what  is  the  other  ? 

Finding  the  area  of  a  trapezium. 

Written  Work 

1.  Find  the  area  of   a  trapezium  whose   diagonal   is    30 

inches,    and    whose    altitudes   are    12    inches    and    8    inches 

respectively. 

Observe:  1.    That  the  area  of  the  trapezium  equals 
the  area  of  its  two  triangles. 

2.  That  the  area  of  one  triangle  equals  \  of  30  x  8 
X  1  sq.  in. 

3.  That  the  area  of  the  other  triangle  equals  h  of 
30  x  12  x  1  sq.  in. 

4.  That  the  area  of  the  trapezium  equals  \  of  30  x  20  x  1  sq.  in.,  or 
300  sq.  in. 

Tfie  area  of  a  trapezium  is  found  Ig  dividing  it  into  tri- 
angles and  finding  the  sum  of  their  areas. 

2.  The  base  line  dividing  a  trapezium  into  two  triangles 
is  40  ft.  The  altitude  of  one  triangle  is  10  ft,,  of  the  other 
is  12  ft.     Find  the  area  of  the  trapezium. 

3.  A  trapezium  is  divided  into  two  triangles  by  a  line  28 
ft.  long.  Find  the  area  of  the  trapezium,  if  the  altitude  of 
one  triangle  is  8  ft.  and  of  the  other  triangle  14  ft. 


THE    CIRCLE 

Observe  the  figure.     What  is  its  shape?    Observe 
that  its  boundary  line  changes  its  direction  regularly 
at  every  point. 

A  circle  is  a  plane  figure  bounded  by  a 
curved  line,  every  point  of  which  is  equally 
distant  from  a  point  within  called  the  venter. 


c^eSsjh. 


HAM.    i  OMPL.     ARJTH. 


■14 


210 


PRACTICAL   MEASUREMENTS 


The  circumference  of  a  circle  is  its  bounding  line. 

A  diameter  is  a,  straight  line  passing  through  the  center 
with  both  ends  terminating  in  the  circumference. 

A  radius  is  a  straight  line  extending  from  the  center  to 
the  circumference. 

Measure  carefully  with  a  cord  the  distance  around  a  circle 
1  foot  in  diameter,  and  you  will  find  it  is  about  3.1416  ft.  in 
circumference.  This  relation  of  diameter  to  circumference 
is  true  of  all  circles. 

The  circumference  of  a  circle  is  found  by  multiplying  the 
diameter  by  3.1416.  This  ratio  is  represented  by  the  symbol 
ir  (pi)- 

The  diameter  of  a  circle  is  found  by  dividing  the  circumfer- 
ence by  3.1416. 

Written  Work 

Find  the  circumference  if  the  diameter  is: 


lOf  ft. 


7.  40  ft.  4  in. 

8.  30  in. 

9.  8  yd.  2  ft.  4  in. 
Radius  =  ? 

Diameter  =  ? 


1.  15  ft. 

2.  25  ft.  5.   12  ft.  6  in. 

3.  60  ft.  6.   25  yd. 

10.  Circumference  equals  25.1328  ft. 

11.  Circumference  equals  125.664  yd. 
Finding  the  area  of  a  circle. 

1st  Methodo 

Examine  the  figure  : 

Observe:    1.   That  the    circle   may  be    considered   as   made   up  of 

triangles  whose  bases  form  the  circum- 
ference. 

2.  That  the  radius  of  the  circle  is 
equal  to  the  altitudes  of  the  triangles. 

3.  That  the  area  of  the  circle  is  equal 
to  the  areas  of  all  the  triangles,  or  £  of 
the  sum  of  their  bases  (circumference) 
by  their  altitude  (radius). 


AREAS 


211 


The  area  of  a  circle  is  found  by  multiplying  the  circumfer- 
ence by  one  half  the  radius. 

2d  Method. 

Examine  the  circle  inscribed  in  the  square. 

Observe  :  1.  That  the  diameter  of  the  circle  is  just 
equal  to  the  side  of  the  square. 

2.  That  much  of  the  surface  of  the  square,  but  not 
all  of  it  lies  within  the  circumference.  Careful  meas- 
urement shows  that  about  .7854  of  the  surface  of  any- 
square  lies  within  the  circumference  of  the  inscribed  circle. 

Tl\e  area  of  a  circle  equals  .7854  of  the  surface  of  the  cir- 
cumscribed square. 

Written  Work 
Circumference  =  C.    Diameter  =  2).    Radius  =  R.    Area  =  A. 
Find  the  area  if  : 

4.  22  =18  ft. 

5.  D  =  20  in. 

6.  22  =  20  in. 
Find  the  area  to  two  decimal  places  if: 

io.    (7=3. 1416  ft.        13.   Z>  =  35yd. 
Li.    C=6.2832rd.       14.22  =  10  ft. 
L2.    C  =  94.248  in.        15.   D  =10  yd. 

19.  A  circle  20  ft.  in  diameter  is  inscribed  in  a  square. 
What  is  the  area  of  one  of  the  corners  within  the  square, 
but  outside  the  limits  of  the  circle  ? 

20.  A  circular  fountain  20  ft.  in  diameter  is  surrounded 
by  a  cement  walk  4  ft.  wide.  How  much  will  the  walk 
cost  at  $1.50  per  square  yard? 

Xote.  —  Find  the  difference  between  the  areas  of  the  two  circles, 
the  first  bounded  by  the  circumference  of  the  fountain,  and  the  second, 
by  the  circumference  of  the  walk. 


1.  2>  =  10  rd. 

2.  R  =  10  rd. 

3.  2>  =  18  ft. 


7.  R  =  40  rd. 

8.  2>  =  25  yd. 

9.  R  =  40  ft. 

16.  R  =  125  ft, 

17.  2)  =120  yd. 

18.  22=19;yd. 


212 


PRACTICAL   MEASUREMENTS 


SOLIDS 

1.  How  many  faces  has  this  solid? 
What  is  their  shape?  How  do  they 
compare  in  size  ? 

A  cube  is  a  solid  bounded  by  six 
equal  square  faces. 

2.  Every  1-inch  cube  rests  on  how 
many  square  inches  of  surface  ? 

3.  Show  that  144    one-inch  cubes 
may  be  placed  on  1  square  foot  of  surface. 

4.  How  many  cubes  would  make  12  such  layers? 

5.  Show  that  1728  cubic  inches  equal  1  cubic  foot. 

6.  How  many  1-inch  cubes  can  be  put  into  a  cubical  box 
whose  edge  is  3  inches? 

7.  How  many  1-foot  cubes  can  be  placed  on  9  square  feet 
of  surface?     (Make  diagram.) 

8.  How  many  cubes  are  there  in  three  such  layers? 

9.  Show  that  27  cubic  feet  equal  1  cubic  yard. 
Learn  this  table  of  solid  or  cubic  measure  : 


1728  cubic  inches  ( 

cu.  in 

)  =  1  cubic  foot  (cu. 

ft.) 

27  cubic  feet  (cu. 

ft.) 

=  1  cubic  yard  (cu 

yd.) 

128  cubic  feet  (cu. 

ft.) 

=  1  cord  of  wood  or  tanbark 

100  cubic  feet  (cu. 

ft.) 

=  1  cord  of  stone 

1  cubic  yard  of  earth  equals  1  load. 

The  unit  of  cubic  measure  is  a  cube  whose  edge  is  one  of 
the  linear  units ;  thus,  a  cube  each  edge  of  which  is  one  inch 
in  length  is  a  cubic  inch. 


SOLIDS 


213 


A  cubic  foot  is  a  cube  whose  edge  is  one  foot. 

A  cubic  yard  is  a  cube  whose  edge  is  one  yard. 

A  cord  of  wood  or  tanbark  is  a  pile  of  4-foot  wood  or  tan- 
bark  8  feet  long  and  4  feet  high. 

A  cord  of  short  wood  is  a  pile  of  short  lengths  8  feet  long 
and  4  feet  high. 

The  number  of  cords  of  short  wood  in  a  pile  is  found  by 
dividing  the  number  of  square  feet  in  one  side  by  32. 


Surface  of  Rectangular  Solids 


How  is  the  surface  of  each  face 
found  ?  How  many  faces  has  this 
solid  ?  Show  that  the  sum  of  the  faces 
in  this  solid  is  the  surface  of  the  solid. 


A  rectangular  solid  is  a  solid  bounded  by  six  rectangular 
surfaces. 

Written  Work 


Find  the  entire  surface  of  : 

Rectangular  Solids 

1.  12  ft.  by  8  ft.  by  G  ft. 

2.  20  ft.  by  10  in.  by  10  in. 

3.  1G  ft.  by  2  ft.  by  1^  ft. 

4.  10  ft.  by  8  ft.  by  7  ft. 

5.  G  ft.  by  5  ft.  by  5  ft, 

6.  13  ft.  by  8  ft.  by  3  ft. 

7.  20  ft.  by  9  ft.  by  7  ft. 


Cubes 

8.  4  inches  on  an  edge. 

9.  12  inches  on  an  edge. 

10.  2  feet  on  an  edge. 

11.  121  inches  on  an  edge. 

12.  14  inches  on  an  edge. 

13.  11|  feet  oil  an  edge. 

14.  \\\  inches  on  an  edge. 


214 


PRACTICAL   MEASUREMENTS 


Volume  of  Rectangular  Solids 


4  in. 


Scale  :  \  inch=  1  in. 


Each  cube  in  the  solid  represents 
one  cubic  inch.  How  man)"  cubic 
inches  are  there  in  the  first  layer  ? 
How  many  such  layers  does  this  solid 
contain?  How  many  cubic  inches 
does  the  solid  contain  ?  Observe 
that  the  product  of  the  three  dimen- 
sions expresses  the  number  of  cubic 
units. 

The  volume  of  a  solid  is  the  num- 
ber of  cubic  units  it  contains. 


If  the  dimensions  are  expressed  in  inches,  the  unit  of  measure  is  1 
cubic  inch  :  if  expressed  in  feet,  the  unit  of  measure  is  1  cubic  foot ;  if 
expressed  in  yards,  the  unit  of  measure  is  1  cubic  yard.  If  the  dimen- 
sions are  expressed  in  related  units,  as  feet  and  inches,  or  yards  and 
feet,  they  must  first  be  changed  to  like  units. 


Written  Work 

1.  Find  the  volume  of  a  rectangular  solid  8  ft.  6  in. 
square  and  12  ft.  4  in.  in  length. 

Thickness  =  8.5  ft. :  width  =  8.5  ft.;  length  =  12J  ft. 

Contents  or  volume  =  S.5  x  8.5  x  12£  x  1  cu.  ft.,  or  891.08$  en.  ft. 

The  volume  of  a  rectangular  solid  is  found  by  multiply ing 
the  unit  of  measure  by  the  product  of  its  three  dimensions  when 
expressed  in  like  units. 

Find  the  contents  or  volume  of  the  following  solids: 

2.  10  ft.  by  6  ft.  3  in.  by  4  ft.         5.   1  yd.  by  2  ft.  by  18  in. 

3.  12  ft.  by  9  ft.  6  in.  by  6  ft.         6.   68  in.  by  1  ft.  by  10  in. 

4.  10  ft.  square  and  S  ft.  high.       7.   5  yd.  by  1 1  yd.  by  2  ft. 


SOLIDS  215 

8.  How  many  loads  of  earth  must  be  removed  in  excavat- 
ing for  a  cellar  30  ft.  by  24  ft.  and  8  ft.  in  depth  ? 

9.  Estimate  the  number  of  cakes  of  soap  3  inches  by  2 
inches  by  2  inches  that  can  be  packed  in  a  box  3  feet  by  2 
feet  by  2  feet. 

10.  A  schoolroom  is  40  ft.  by  28  ft.  by  16  ft.  How  many 
cubic  feet  of  air  space  are  there  for  each  of  39  pupils  and 
their  teacher  ? 

11.  How  many  cords  of  4-foot  wood  are  there  in  a  pile 
40  ft.  long  and  4  ft.  high  ? 

12.  Estimate  the  number  of  cords  of  18-inch  wood  in  3 
piles  each  60  ft.  long  and  4  ft.  high. 

13.  How  many  cubical  boxes  3  ft.  6  in.  on  an  edge  can  be 
placed  in  a  storage  room  14  ft.  in  length,  width,  and  height  ? 

In  a  certain  township,  the  piles  of  20-inch  wood  in  the 
yards  of  four  schools  were  as  follows  : 

14.  Sykes, 

15.  Graham, 

16.  Wilson, 

17.  Clark, 

Estimate  the  number  of  cords  at  each  school  and  the 
value  of  the  wood  at  $1.85  per  cord. 

18.  Find  the  number  of  loads  of  earth  removed  in  exca- 
vating for  a  cellar  16  feet  wide,  30  feet  long,  and  6  feet  in 
depth. 


of  Piles 

Length  of  Piles 

60  ft. 
40  ft. 

Height  of  Piles 

4  ft. 
6  ft. 

<2 

u 

50  ft. 
60  ft. 

5  ft. 
4  ft. 

\\ 

72  ft. 
45  ft. 

5  ft. 

6  ft. 

\l 

36  ft. 
60  ft. 

5  ft. 
4  ft. 

216  PRACTICAL  MEASUREMENTS 

19.  A  pile  of  tanbark  is  8  ft.  wide,  9  ft.  high,  and  100  ft. 
long.     Find  the  number  of  cords. 

20.  A  cubical  block  of  granite  2  ft.  on  an  edge  is  what 
part  of  a  cubical  block  of  granite  6  ft.  on  an  edge  ? 

When  possible,  use  cancellation  in  the  following  problems  : 

21.  Cape  Cod  cranberries  are  shipped  in  a  crate  whose 
inside  dimensions  are  20  in.  x  10|^  in.  x  6|  in.  How  many 
cubic  inches  are 'there  in  a  crate  ? 

22.  Sweet  potatoes  are  sometimes  sold  in  a  box  19^  in.  x 
llf  in.  x  10  in.  How  much  does  this  differ  from  a  bushel 
(2150.4  cu.  in.)? 

23.  Colorado  apples  are  sometimes  shipped  in  a  box  18  in. 
X  11 J  in.  x  11  in.  How  many  cubic  inches  more  or  less 
than  a  bushel  does  such  a  box  contain  ? 

24.  Colorado  apples  are  sometimes  shipped  in  a  box  16 
in.  x  11 1  in.  x  8|  in.  How  many  cubic  inches  does  such  a 
box  contain  ? 

25.  California  celery  is  shipped  in  crates  24^  in.  x  22  in. 
X  20£  in.     How  many  cubic  inches  are  there  in  such  a  crate  ? 

26.  California  dates  are  sold  in  boxes  17|  in.  x  10  in.  x 
9^  in.     How  many  cubic  inches  are  there  in  such  a  box  ? 

27.  Figs  are  packed  solid  in  a  box  12  in.  x  9  in.  x  If  in. 
How  many  cubic  inches  are  there  in  such  a  box  ? 

28.  The  standard  California  orange  box  is  now  24  in. 
x  11^  in.  X  12  in.  Tangerines  are  shipped  in  boxes  24  in. 
x  12  in.  x  6|  in.     Which  is  the  larger,  and  how  many  cubic 

inches  larger  is  it  ? 

29.  How  many  cubic  inches  are  there  in  a  box  5|  in.  x 
8|  in.  x  2|  in.  ?  Find  the  number  of  cubic  inches  in  a  box 
81  in.  x  12i  in.  x  44  in. 


LUMBER 


217 


One  Board  Foot 


LUMBER 

Measurement  of  lumber. 

Lumber  is  any  kind  of  sawed  timber  as  boards,  planks, 
sills,  etc.  The  unit  of  lumber  measure  is  the  board  foot;  it 
is  a  board  1  foot  long,  1  foot  wide,  and  1 
inch  thick.      Draw  it. 

Note.  — Boards  less  than  1  inch  in  thickness  are 
measured  as  if  they  were  1  inch  thick ;  boards  over 
1  inch  in  thickness  are  measured  by  their  actual 
thickness  in  inches  and  fractions  of  an  inch. 

1.  How  many  board  feet  are  there  in  a  board  1  foot 
wide,  1  inch  thick,  and  3  feet  long?  5  feet  long?  9  feet 
long  ? 

2.  How  many  board  feet  are  there  in  a  board  6  inches 
wide,  1  inch  thick,  and  3  feet  long?  10  feet  long?  In  a 
board  6  inches  wide,  \  inch  thick,  and  12  feet  long? 

3.  How  many  board  feet  are  there  in  a  sill  5  feet  long,  1 
foot  wide,  and  4  inches  thick  ? 

5  ft. 


Written  Work 

1.  Find  the  number  of  board  feet  in  a  sill  18  ft.  long, 
10  in.  wide,  and  8  in.  thick. 

10  in.=  |  ft.  One  surface  =  18  x  |  x  1  hoard  foot,  or  15  board  feet. 
The  sill  contains  8  x  15  board  feet,  or  120  board  feet. 

The  number  of  board  feet  in  a  piece  of  lumber  is  found  by 
multiplying  the  number  of  board  feet  in  one  surface  by  the 
number  of  inches  in  thickness. 


218  PRACTICAL   MEASUREMENTS 

Find  the  number  of  board  feet  in  the  following: 

2.  1  board,  10  ft.  long,  11  ft.  wide,  and  1  in.  thick. 

3.  1  board,  16  ft.  long,  11  ft.  wide,  and  |  in.  thick. 

4.  2  boards,  each   16   ft.   long,   1   ft.  wide,    and    |    in. 
thick. 

5.  6  boards,  15  ft.  x  2  ft.  x  1  in. 

6.  4  boards,  16  ft.  x  1|  ft.  x  -|-  in. 
How  many  feet  of  lumber  are  there  in : 

7.  1  plank,  12  ft.  long,  1  ft.  wide,  and  3  in.  thick  ? 

8.  1  sill,  15  ft*  long,  1^  ft.  wide,  and  8  in.  thick  ? 

9.  4  planks,  12  ft.  long,  1|  ft.  wide,  and  2  in.  thick  ? 

10.  2  pieces,  18  ft.  by  1  ft.  by  1  ft.? 
Find  the  number  of  feet  of  lumber  in : 

11.  10  planks,  each  8  ft.  long,  1^  ft.  wide,  and  3  in.  thick. 

12.  12  sills,  each  20*  ft.  long  and  10  in.  square. 

13.  20  joists,  each  12  ft.  long,  12  in.  wide,  and  3  in.  thick. 

14.  3  beams,  each  40  ft.  long  and  10  in.  by  12  in. 

15.  30  scantlings,  each  16  ft.  long  and  2  in.  by  3  in. 

16.  How  much  will  the  flooring  for  two  rooms,  each  18  ft. 
x  20  ft.,  cost  at  $30  per  M.? 

Buying  and  selling  lumber. 

Lumber  is  bought  and  sold  by  the  thousand  board  feet. 
In  practice  the  cost  is  computed  at  so  much  per  board  foot  ,• 
thus,  $20  per  thousand  feet  (M.)  is  $.02  per  board  foot. 

Show  that  $35  per  M.  =  $.035  per  board  foot. 
$60  per  M.  =  $.06  per  board  foot. 


LUMBER  219 

Written  Work 

1.  Estimate  the  cost  of  378  feet  of  oak  at  $26  per  M.; 
of  6389  ft.  white  pine  at  $48  per  M.;  of  972  ft.  cherry  at 
$72  per  M.;  of  693  ft.  white  ash  at  $47  per  M. 

Find  the  cost  at  $35  per  M.  of: 

2.  50  hoards,  16  ft.  long,  12  in.  wide,  and  1  in.  thick. 

3.  60  hoards,  12  ft.  long,  15  in.  wide,  and  1|  in.  thick. 

4.  100  boards,  15  ft.  long,  6  in.  wide,  and  f  in.  thick. 

5.  75  boards,  18  ft.  long,  10  in.  wide,  and  1  in.  thick. 

6.  45  boards,  16  ft.  long,  5  in.  wide,  and  1  in.  thick. 

Short  forms  are  used  by  carpenters,  architects,  and  mechanics  ;   thus, 
one  mark  (')  represents  feet,  and  two  marks  (")  represent  inches. 

Find  the  number  of  board  feet: 

7.  120  studding,  2"  x  4"  x  12'. 

8.  400  planks,  2"  x  1'  x  16'. 

9.  300  boards,  1"  x  10"  x  14'. 
10.  600  boards,  1"  x  6"  x  16'. 
li.  100  boards,  f  "  x  12"  x  16'. 

12.  15  sills,  6"  x  10"  x  20'. 

13.  250  joists,  2"  x  8"  x  24'. 

14.  70  sills,  10"  x  12"  x  30'. 

15.  125  sleepers,  3"  x  10"  x  28'. 

16.  200  boards,  J"  x4'"x  16'. 

17.  500  joists,  21"  x  8"  x  20'. 

18.  325  planks,  3"  x  14"  x  16'. 

19.  300  sills,  5"  x  8"  x  24'. 

20.  50  posts,  10"  x  12"  x  14'. 

21.  400  studding,  2"  x  3"  x  18'. 

22.  500  beards,  11"  x  10"  X  16'. 


220  PRACTICAL  MEASUREMENTS 

23.  Estimate  the  cost  of  the  planks  in  examples  8  and  18, 
at  $.027  per  board  foot. 

24.  Estimate  the  cost  of  the  sills  in  examples  12,  14,  and 
19,  at  $.032  per  board  foot. 

25.  Estimate  the  cost  of  the  studding  in  examples  7  and 
21,  at  $.026  per  board  foot. 

CONCRETE,   STONE,  AND  BRICKWORK 

Concrete  work  is  estimated  by  the  cubic  yard. 

Stone  work  is  estimated  by  the  perch,  of  24.75  cu.  ft.,  or 
by  the  cord  of  100  cu.  ft.  Stones  are  often  sold  by  the  pound. 
3200  pounds  are  estimated  to  lay  1  perch. 

In  estimating  either  contract  work  or  cost  of  labor,  in  concrete  and 
stone  work,  the  distance  around  the  wall  is  considered  the  length.  In 
cases  where  there  are  inside  corners,  however,  as  at  a  and  b  in  the 
figure  on  p.  226,  add,  for  each  inside  corner,  twice  the  thickness  of  the 
wall.  This  measures  all  corners  twice.  In  estimating  material,  deduct 
for  openings  and  measure  the  corners  but  once. 

Range  work  and  lintels  are  measured  by  the  linear  foot. 

Brickwork  is  estimated  by  the  thousand.  Bricks  vary  in 
size,  but  they  are  usually  8"  by  4"  by  2". 

In  estimating  the  number  of  bricks  in  a  wall,  measure  the  corners 
once,  deduct  all  openings,  and  multiply  the  number  of  square  feet  re- 
maining in  the  surface  by  7  when  the  wall  is  1  brick  thick;  by  14  when 
the  wall  is  2  bricks  thick ;  and  by  21  when  the  wall  is  3  bricks  thick. 

Written  Work 

1.  Find  the  number  of  cords  of  stone  in  a  breakwater 
200  ft.  long,  14  ft.  wide,  and  16  ft.  high. 

2.  A  building  150  ft.  by  130  ft.  has  a  concrete  foundation 
4  ft.  in  width  and  10  ft.  in  depth  below  the  structural  iron. 
Estimate  the  number  of  cubic  yards  of  material  used. 


THE   CYLINDER  221 

3.  If  the  cement,  the  gravel,  and  the  sand  are  in  the  ratio 
of  1,  5,  and  2,  find  the  number  of  loads  of  gravel  and  of  sand 
used  in  the  construction  of  the  foundation  in  example  2. 

4.  Estimate  the  contract  cost  of  the  concrete  work  at 
$7.75  per  cubic  yard. 

5.  Estimate    the    number    of  ^^.^^..^..^.^.^....^^ 

cubic   yards  of  concrete  in  this   M?-_    ....    —     .:.  ;.,        .  .  . 

retaining  wall.  ^;Y. ',' '•'.".  . '-•  / '.^v ■;•;•  ■.] 

6.  The  walls  of  a  brick  house  ^gfc '.•'•'••;     .':"•:!  ^:  ■■■'.. 
36  ft.  long,  24  ft.  wide,  and  18  ft.                            200' 

high  are  13  in.  or  3  bricks  thick. 

Estimate  the  number  of  bricks  required  for  the  walls,  allow- 
ing for  11  windows  averaging  3±  ft.  by  6  ft.,  and  2  doors 
averaging  3|-  ft.  by  7  ft. 

7.  A  house  whose  walls  are  9  in.  or  2  bricks  thick  is  40 
ft.  long,  30  ft.  wide,  and  24  ft.  high.  Estimate  the  number 
of  bricks  required  for  the  walls,  allowing  for  12  windows 
3  ft.  by  7  ft.,  and  3  doors  3|  ft.  by  8  ft. 

8.  The  stone  work  for  the  foundation  of  a  house  28  ft. 
by  38  ft.  is  1*  ft.  in  thickness  and  6  ft.  in  height  to  the 
range  work.  Estimate  the  cost  of  the  stone  work  at  $6.30 
a  perch,  and  the  range  work  along  the  two  sides  and  the 
rear  at  60  cents  per  linear  foot. 

THE  CYLINDER 

Examine  this  solid.  ^SlS=s 

How  many  ends  or  bases  has  it?     What  is  the  shape 

of  each?     Are   the  bases   equal   and   parallel?     Describe 

the  shape  of  the  body. 

A    cylinder    is    a    solid    whose    two  bases  are 
equal  and  parallel  circles  and  whose  diameter  is    | 
uniform. 


000 

—  —  — 


PRACTICAL   MEASUREMENTS 


The  convex  surface  of  a  cylinder  is  the  lateral  or  curved 
surface.  The  altitude  is  the  perpendicular  distance  between 
its  two  bases. 

Examine  this  cylinder. 

Observe:  1.  That  if  a  piece  of 
paper  is  fitted  to  cover  its  convex  sur- 
face and  then  unrolled,  its  form  will 
be  that  of  a  rectangle. 

2.  That  the  circumference  of  the 
base  is  the  length  of  the  rectangle, 
and  the  altitude  of  the  cylinder  is  the 
width  of  the  rectangle. 

The  convex  surface  of  a  cylinder  is  found  by  multiplying  the 
unit  of  measure  by  the  product  of  the  circumference  and 
the  altitude. 

The  entire  surface  of  a  cylinder  is  found  by  adding  the  area 
of  the  bases  to  the  convex  surface. 

• 

Written  Work 

Find  the  convex  surface  of  a  cylinder: 

1.  D.  10  in.,  height  24  in.  4.    D.  20  in.,  height    4  ft. 

2.  D.  15  in.,  height  30  in.  5.    D.     8  in.,  height    4  ft. 

3.  D.     2  ft.,  height  10  ft.  6.    D.     6  ft.,  height  15  ft. 
Find  the  entire  surface  of  : 

7.    A  water  tank  12  ft.  in  diameter  and  12  ft.  in  height. 
A  steam  boiler  15  ft.,  long  and  3  ft.  in  diameter. 
Find  the  volume  of  a  cylinder  3  ft.  in  diameter  and  5  ft. 
high. 

Observe:     1.    That  the  area  of  the  base  is  32  x  .7854 
x  1  sq.ft.,  or  7.0686  sq.  ft. 

2.  That  the  first  row  of  cubic  units  contains  7.0686 
cu.  ft. 

3.  That  the  cylinder  contains  5  times  7.0686  cu.  ft.,  or 
35.343  cu.  ft. 


8. 
9. 


BINS,   TANKS,    AND   CISTERNS  223 

The  volume  of  a  cylinder  is  found  by  multiplying  the  unit 
of  measure  by  the  urea  of  the  base  and  this  product  by  the 
height  of  the  cylinder. 

Find  the  volume  of  a  gas  tank,  silo,  cistern,  etc.  : 

10.  D.  15  ft.,  height  18  ft.         14.    R.  2  ft.,  depth  8  ft. 

11.  D.  25  ft.,  height  30  ft.         15.    R.  8  ft,,  height  30  ft. 

12.  D.  16  ft.,  height  20  ft.         16.    D.  1  ft.,  length  16  ft. 

13.  D.  20  ft,,  depth  15  ft.  17.   D.  5  ft.,  length  12  ft. 

BINS,  TANKS,  AND  CISTERNS 

Wheat  and  other  grains  are  generally  sold  by  weight,  but 

the  capacity  of  bins  is  often   estimated    in   bushels.     The 

capacity  of  tanks  and  cisterns  is  estimated  in  gallons  or 

barrels. 

Note.  —  The  standard  bushel  in  the  United  States  contains  2150.42  cu- 
bic inches,  stricken  measure,  and  2747.71  cubic  inches  heaped  measure. 
231  cu.  in.  =  1  gal.        31  \  gal.  =  1  bbl.  when  estimating  contents. 

Written  Work 

Find  contents  in  bushels  of  : 

1.  A  bin  20  ft.  by  10  ft.  by  5  ft. 

2.  A  box  12  ft.  x  9  ft.  x  6  ft. 

3.  A  metal  trough  for  watering  cattle  is  12  ft.  long,  3  ft. 
wide,  and  20  in.  deep.  Estimate  the  number  of  gallons  it 
holds. 

4.  A  cistern  tank  for  a  windmill  pump  is  8  ft.  in  di- 
ameter and  10  ft.  in  depth.  Estimate  the  number  of  barrels 
of  water  it  holds. 

5.  The  rainfall  on  a  certain  day  was  1\  inches.  Find 
the  number  of  barrels  of  water  that  fell  on  Mr.  Anderson's 
flower  plot  which  is  20  ft.  long  and  10  ft.  wide. 


224  PRACTICAL  MEASUREMENTS 

APPROXIMATE   MEASUREMENTS 

Approximate  equivalents  of  the  following  measures  are 


1  bu.  shelled  grains 

= 

1]  cu.  ft. 

1  bu.  apples,  coal,  roots,  corn  in  ear,  etc. 

= 

If  cu.  ft. 

1  bbl.  in  estimating  contents 

= 

4i  cu.  ft. 

1  cu.  ft.  of  water 

= 

62]  lb. 

1  gal.  of  water 

= 

81  lb. 

1  cu.  ft.  of  any  liquid 

= 

7.i  gal. 

1  ton  of  hay  well  packed 

= 

450  cu.  ft. 

1  ton  of  clover  hay 

= 

550  cu.  ft. 

1  ton  of  bituminous  coal 

= 

42  cu.  ft. 

1  ton  of  hard  coal 

= 

35  cu.  ft. 

Written  Work 

1.  A  water  meter  registered  900  gallons  of  water  con- 
sumed in  a  month.  Estimate  the  weight  of  the  water  used, 
and  its  volume  in  cubic  feet. 

2.  The  inside  measurement  of  a  wagon  box  is  12  ft.  4  in. 
by  3  ft.  6  in.  by  16  in.  Estimate  the  number  of  tons,  etc., 
of  anthracite  coal  it  would  contain;  the  number  of  tons,  etc., 
of  soft  coal. 

3.  The  rainfall  on  a  roof  20  ft.  by  30  ft.  during  April 
and  May  was  9.5  in.  Find  the  weight  of  the  water  that  fell 
on  the  roof  during  that  time. 

4.  A  swimming  pool  is  80  ft.  long,  60  ft.  wide,  and  5  ft. 
deep.     Estimate  the  number  of  barrels  of  water  in  the  pool. 

5.  Estimate  the  number  of  bushels  in  an  oat  bin  14  ft. 
long  and  10  ft.  wide  if  the  bin  is  filled  with  oats  to  a  depth 
of  6  feet. 


REVIEW   PROBLEMS  225 

6.  I  Tow  many  tons  of  hard  coal  are  there  in  a  bin  16  ft.  x 
12  ft.,  when  the  pile  is  1  ft.  high  ? 

7.  There  are  5  ft.  of  water  in  a  cistern  4  ft.  in  diameter. 
How  many  gallons  of  water  are  there  in  the  cistern? 

8.  Find  the  weight  of  the  water  in  a  railroad  tank  12  ft. 
in  diameter  and  16  ft.  in  depth,  if  the  tank  has  12  ft.  of 
water  in  it. 

9.  How  many  bushels  of  wheat  can  be  shipped  in  a  car 
whose  inside  measurements  are  36  ft.  by  8  ft.  6  in.  by 
8  ft.  ? 

10.  Estimate  the  number  of  tons  of  clover  hay  in  a  mow 
60  ft.  by  18  ft.  by  16  ft.  Estimate  the  number  of  tons  of 
timothy  hay  in  the  same  mow. 

REVIEW   PROBLEMS 

1.  A  field  containing  20  acres  is  61  rods  long.  How  wide 
is  it? 

2.  The  area  of  the  floor  of  a  schoolroom  contains  1120  sq. 
ft.  The  air  in  the  room  occupies  16800  cu.  ft.  What  is  the 
height  of  the  ceiling  ? 

3.  How  many  tiles  6  in.  square  are  required  for  a  hall  40 
ft.  by  20  ft.  6  in.? 

4.  The  side  of  a  square  is  20  inches.  Find  its  area;  its 
perimeter. 

5.  The  edge  of  a  cube  is  18  inches.  Find  its  surface;  its 
contents. 

6.  How  many  cubical  boxes  whose  edges  are  6  in.  can  be 
put  into  a  box  8  ft.  6  in.  by  4  ft.  6  in.  by  3  ft.? 

7.  How  many  cakes  of  soap  2  in.  x  2  in.  x  4  in.  may  be 
packed  in  a  box  2  ft.  long,  1  ft.  wide,  and  1  ft.  high? 

HAM.    t  OMl'L.     A  HI  III.  —  15 


226 


PRACTICAL   MEASUREMENTS 


14 

Elii'iiiii I* 


Miniii nun 


;  O 


8.  The  edges  of  two  cubes  are  respectively  10  inches  and 
12  inches.     How  much  more  surface  has  one  than  the  other? 

9.  Find  the  cost  of  a  farm,  480  rods  long  and  320  rods 
wide,  at  860  per  acre. 

10.  How  much  will  it  cost  to  put  a  wire  fence  around  this 
farm  at  50  0  per  rod  ? 

11.  A  ranchman  bought  one  square  mile  of  land  at  $10 
per  acre.  He  put  a  fence  around  it  and  then  divided  it  by 
fences  into  four  equal  square  farms  for  his  sons.  Find  the 
entire  cost  if  the  fence  cost  $.40  per  rod. 

12.  Estimate  the  contract  price  of 
building  this  cellar  wall  18  in.  thick 
and  6^  ft.  in  height  at  $5.95  a  perch. 

Distance  around  the  wall  =  164  ft. 
Add  to  this  distance  twice  the  thickness  of 
the  wall  for  each  of  the  inside  corners,  a  and 
\^)  6;   that   is,  twice  2  x  18  in.,  or  6  ft.     Then, 
the  length  of  the  wall  with  8  corners  counted 
twice  =  164  ft.  +  6  ft.  =  170  ft.     The  volume 
of    the    wall  =  170  x  6 J  x  U  x  1    cu.    ft.  = 
1657.5  cu.  ft.     The  number  of  perch  of  stone 
=  1657£  -h  24|  =  66f|  perch.     The   cost  of  the  wall  =  66ff  x  $5.95  = 
$398.47. 

Query.  —  Why  are  the  8  corners  measured  twice  ? 

13.  Estimate  the  number  of  bricks  necessary  for  a  dwell- 
ing erected  on  the  foundation  as  given  in  example  12,  if  the 
walls  are  3  bricks  (13  in.)  thick  and  20  feet  in  height,  mak- 
ing an  allowance  of  150  square  feet  for  openings. 

Query.  —  Why  are  the  8  corners  measured  once  ? 

14.  Estimate   the  cost  of  the  face  brick  for   the   above 

dwelling  at  $16.50  per  thousand  and  $9.00  per  thousand  for 

laying. 

Note.  —  Consider  the  face  brick  as  a  wall  4  in.  thick  and  measure  the 
8  corners  once. 


11 IIIIIIITTTT 


I1    MM. I, 


40' 


REVIEW   PROBLEMS  227 

15.  A  level  lot  60  ft.  by  120  ft.  has  erected  on  it  a  dwell- 
ing otj  ft.  by  42  ft.  If  the  excavating  averages  5  ft.  and  the 
removed  earth  is  placed  on  the  lot,  to  what  height  will  it 
raise  the  grade  of  the  lot  ? 

16.  A  certain  town  has  a  cylindrical  water  tank  20  ft.  in 
diameter  and  45  ft.  in  height.  The  gauge  shows  30  ft.  of 
water  in  the  tank.     Estimate  the  weight  of  the  water. 

17.  How  many  yards  of  carpet,  27  in.  wide,  are  required 
for  a  room  24  ft.  by  20  ft.  3  in.  ?  Strips  are  to  run  length- 
wise. 

18.  How  much  will  it  cost  to  carpet  a  room  24  feet  square 
with  carpet  27  inches  wide,  at  $1.25  per  yard,  allowing  10 
inches  on  each  strip  except  the  first  for  matching  ? 

19.  How  much  will  it  cost  to  plaster  a  room  20  ft.  by  16 
ft.,  and  12  ft.  to  the  ceiling,  at  20^  per  square  yard,  allowing 
for  one  door  3 J  ft.  by  7  ft.,  and  2  windows,  each  4  ft.  by 
6  ft.  ?  700  ft. 

20.  This  plot  of  ground  is  700  ft.  long    | Qak'St_ 

and  (500  ft.  wide.  Find  the  cost  of  grading 
streets  40  ft.  in  width  run  through  the  cen- 
ter each  way,  as  here  shown,  at  $1.90  per 
linear  yard.  Find  the  amount  from  the  sale 
of  lots  30'  x  140'  facing  on  Oak,  Center, 
and  Clark  Streets,  at  $  20  per  front  foot.  ..C/arkSt,. 

21.  Each  of  the  three  sides  of  a  triangle  is  50  ft.  What 
is  the  size  of  each  of  its  angles  ?     Draw  the  figure. 

22.  The  sides  of  a  triangle  are  80  fr.,  80  ft.,  and  30  ft. 
respectively.  If  the  angle  opposite  the  short  side  is  24°, 
what  is  the  size  of  each  of  the  other  angles  ?  Draw  the 
figure. 


Cet 

itt 

>rSt 

228 


PRACTICAL   MEASUREMENTS 


Oo 
O 


23.  The  angle  opposite  one  of  the  equal  sides  of  an  isos- 
celes triangle  is  75°.     Find  the  size  of  the  other  two  angles. 

24.  One  angle  in  a  right  triangle  is  13.75°.  Find  the 
other  two  angles. 

25.  The  angle  opposite  the  base  in  an  isosceles  triangle 
is  18^°.     What  is  the  size  of  the  other  two  angles  ? 

26.  A  railroad  com- 
pany owns  a  strip  of  land 
in  the  form  of  a  parallel- 
ogram, 66  ft.  wide  and 
92.78  +  rd.  long  through 
this  farm.  Find  the 
area  of  A  and  the  area 
of  the  part  owned  by  the 
railroad.  How  can  the 
area  of  B  be  found  ? 

27.  A  wheel  is  3  ft. 
in  diameter.     How  many 

revolutions  will  it  make  in  moving  forward  942.48  ft.? 

28.  The  speed  of  a  vessel  for  5  hours  was  23.17  knots  per 
hour.     Find  her  average  speed  per  hour  in  statute  miles. 

29.  Lead  is  11.35  times  as  heavy  as  water.  Find  the 
value  of  a  cubic  foot  of  lead  at  5  ^  per  pound. 

30.  How  many  rolls  of  paper  are  required  for  a  room  20  ft. 
X  18  ft.,  and  13  ft.  3  in.  from  the  top  of  the  baseboard  to 
the  ceiling,  allowing  for  2  windows  3^  ft.  in  width  and  one 
door  3^  ft.  wide  (papering  the  ceiling  lengthwise)  ? 

31.  The  base  of  a  triangle  is  30  ft.  and  its  altitude  23  ft. 
Find  its  area. 

32.  A  barn  is  80  ft.  by  50  ft."  It  is  40  ft.  to  the  base  of 
the  gable  and  58  ft.  to  the  top  of  the  gable.  How  much  will 
it  cost  to  paint  it  at  8  ^  per  square  yard  ?  . 


<. lOOrd.- 

-65rd Z 

w 

<£>\  \ 

<s>\  \ 

,-.       "—A  \ 

B         cp\  \ 

\        A 

-v\ 

— ^  \ 

o-\ 

\l8rd. 

REVIEW   PROBLEMS  229 

33.  If  the  slope  of  the  roof  of  the  barn  in  problem  32  is 
32  ft.  long,  and  it  projects  1|  ft.  at  each  end,  how  much 
will  it  cost  to  roof  it  at  $  8  per  square? 

34.  A  schoolroom  is  40  ft.  long  and  30  ft.  wide.  Estimating 
450  cubic  feet  of  air  to  each  person,  what  should  be  the  height 
of  the  room  to  accommodate  39  pupils  and  their  teacher  ? 

35.  Find  the  cost  of  a  stone  wall  30  ft.  long,  2|  ft.  thick, 
and  6  ft.  high,  at  $5.30  a  perch. 

36.  How  much  will  it  cost  to  cement  the  floor  of  a  cellar, 
40  ft,  by  20  ft.,  at  90^  a  square  yard? 

37.  A  street  50  ft.  from  curb  to  curb  is  opened  for  a  dis- 
tance of  300  yards.  How  much  will  it  cost  to  excavate  it 
to  a  depth  of  1  foot  at  40  ^  per  cubic  yard  ? 

38.  How  much  will  the  curb  of  this  street  cost  at  26^ 
per  linear  foot  ? 

39.  The  sidewalk  on  this  street  is  12  ft.  wide,  including 
a  curb  of  8  inches.  How  much  will  the  brick  for  the  walk 
cost,  at  $  9  per  thousand,  if  the  exposed  surface  of  a  brick  is 
4  in.  x  8  in.  ? 

40.  A  farmer  built  a  circular  silo  12  ft.  in  diameter  and 
24  feet  high.     Find  its  contents  in  cubic  feet. 

41.  How  many  blocks  of  ice,  2  ft.  x  1  ft.  x  1  ft.,  can  be 
packed  in  a  ear  0  ft,  x  8  ft.  x  40  ft.  ?  Ice  is  .92  as  heavy 
as  water.  Find  the  weight  of  the  ice  if  a  cubic  foot  of  water 
weighs  62|  lb. 

42.  A  cistern  is  4  ft,  in  diameter  and  6  ft.  deep.  How 
many  barrels  of  water  will  it  contain  ? 

43.  Estimate  the  weight  of  the  water  in  a  tank  8  ft.  long, 
6  ft.  wide,  and  2  ft.  deep. 

44.  A  vault  is  5  ft.  square  and  G  ft.  deep.  How  much 
will  it  cost  to  cement  the  sides  and  bottom  at  $  .50  per  sq.  ft.  ? 


230 


PRACTICAL   MEASUREMENTS 


45.  A  circular  amusement  park  is  80  rods  in  diameter. 
Find  the  cost  of  the  boards  for  a  tight  board  fence  8  ft.  high, 
inclosing  the  park,  at  $  20  per  M. 

46.  A  corner  lot  in  Seattle  is  25  ft.  by  100  ft.  At  $  25 
per  M.,  what  will  be  the  cost  for  2-inch  plank  for  a  10-foot 
sidewalk  in  front  and  on  the  side,  including  the  corner  ? 

Note.  —  Illustrate  by  diagram. 

47.  Mr.  Ames  owns  a  50-ft.  lot  fronting  on  a  street  60  ft. 
wide  from  curb  to  curb.  The  law  compels  him  to  pay  ^  of 
the  cost  of  paving  the  street  in  front  of  his  lot.  How  much 
will  it  cost  at  $  2.90  per  square  yard  ? 

48.  A  tank  open  at  the  top  is  50  ft.  long,  4  ft.  wide,  and 
3  ft.  deep.  How  much  will  the  lead  for  lining  it  cost,  at  8  ^ 
per  pound,  estimating  4  pounds  to  a  square  foot  ? 

49.  Clay  weighs  1.2  as  much  as  the  same  volume  of  water. 
Estimate  the  weight  of  a  load  of  clay. 

j j'  50.    Find  the  cost  of 

painting  the  sides  and 
ends  of  this  hay  barn 
at  15^  per  square  yard, 
and  the  cost  of  stain- 
ing the  roof  at  12^  per 
square  yard. 

51.  In  excavating  for  a  cellar  60  ft.  long,  30  ft.  wide, 
and  8  ft.  deep,  the  material  was  evenly  distributed  over  a  lot 
90  ft.  by  40  ft.     To  what  depth  was  the  lot  covered  ? 

52.  A  two-story  school  building  has  8  rooms  30  ft.  x  32  ft. 
and  a  hallway  28  ft.  x  15  ft.,  on  each  floor.  How  much 
will  the  flooring  for  the  building  cost  at  $44  per  M.  ? 

53.  In  digging  a  sewer  31  ft.  in  width  and  8  ft.  deep, 
1244|  cubic  yards  of  earth  were  excavated.  Find  the  length 
of  the  sewer  in  feet. 


Test: 

8  +  4  = 
-4 

:12 

-4 

5.    8- 

8 
-2  =  6 

=  12- 

-4 

ANALYSIS 

THE   EQUATION 

l.    8=8  2.    8  +  4=12  3.    8  =  12-4 

In  example  (1)  we  have  an  equal  number  on  each  side 
of  the  equality  sign.  In  example  (2)  we  have  8  +  4  =  12  ; 
but  in  example  (3),  in  order  to  preserve  the  equality,  when 
we  take  4  from  the  left  of  the  equal- 
ity sign  in  example  (2),  we  must  sub- 
tract 4  from  the  number  on  the  right 
of  the  equality  sign.  Thus,8=  12  —  4. 

4.    8  =  6  +  2 

Observe  that  a  number  may  be  moved  from  one  side  of  an 
equation  to  another  by  changing  its  sign. 

Written  Work 

Change  the  following  so  that  the  first   number   in   each 
problem  will  stand  alone  at  the  left  of  the  equality  sign  : 

6.  20  -  10  =    10  10.      75  -  20  =  55 

7.  40-15=   25  n.      85-    5-10=70 

8.  80  +  15  =    95  12.      90  -  10  +    5  =  85 

9.  100  +  75  =  175  13.    100  +  10  -  20  =  90 

14.    First  add,  then  subtract,  5  from  each  member  of  the 
equation  10  =  10. 

(a.)    10  =    10  (b.)    10  =    10 

+  5  =  +5  -5  =  —5 

15=    15  5=      5 

The  same  number  may  h?  added  to  or  subtracted  from  both 
sides  of  an  equation  without  dest roying  the  equality. 

231 


232  ANALYSIS 

Factors  and  their  Product 

1.  5  times  a  certain  number  is  35.    What  is  the  number  ? 

Factors  Product 

5  x  the  number  =  35 
The  number  =  35  -=-  5  =  7 

When  the  product  of  two  factors  is  divided  by  one  of  the 
factors,  the  quotient  is  the  other  factor.  When  one  of  the  factors 
is  unknown,  it  may  be  found  by  dividing  the  product  by  the 
known  factor. 

State  the  factors  and  solve : 

2.  5  times  John's  money  =  $  40.  How  many  dollars  has  he? 

3.  2  times  A's  sheep  are  60.     How  many  sheep  has  he  ? 

4.  6  times  B's  age  is  360  years.     How  old  is  he  ? 

5.  l  of  a  number  is  150.     What  is  the  number? 

6.  1.25  times  a  number  is  30.     What  is  the  number? 

7.  .75  of  a  number  is  75.     Find  the  number. 

8.  ^  of  a  number  is  75.     Find  the  number. 

I  of  the  number  =  75 

The  number        =  3  x  75  =  225 

The  work  may  be  shortened  by  calling  the  unknown 
factor  x.     For  example, 

9.  Mr.  Brown's  profits  equal  4  times  Mr.  Long's  profits, 
and  together  their  profits  are  8 125.     Find  the  profits  of  each. 

Let  x  =  Mr.  Long's  profits. 

4  x  =  Mr.  Brown's  profits 

5  x  =  $125,  or  the  profits  of  both. 
x  =  825,  Mr.  Long's  profits. 

4  x  =  $  100,  Mr.  Brown's  profits. 

10.  Mr.  Byers  and  Mr.  Boydson  together  have  240  acres 
of  land,  and  Mr.  Byers  has  40  acres  more  than  Mr.  Boydson. 
How  many  acres  has  each? 


THE   EQUATION  233 

Let  x  =  the  number  of  acres  in  Mr.  Boydson's  farm. 
x  +  i()  =  the  number  of  acres  in  Mr.  Byers's  farm. 

2  x+  40  =  the  number  of  acres  in  both  farms,  or  240  acres. 
2  x  =  240-40 
2x  =  200 
x  =  100,  the  number  of  acres  in  Mr.  Boydson's  farm. 
x  +  40  =  140,  the  number  of  acres  in  Mr.  Byers's  farm. 

Solve  first  by  written  analysis,  then  orally  : 

11.  Four  times  my  money  and  $6  more  is  $50.  How 
much  money  have  I  ? 

12.  $80  is  $5  more  than  twice  the  cost  of  a  bicycle.  Find 
the  cost. 

13.  Harry's  age  plus  |  his  age  plus  6  years  equals  30 
years.     How  old  is  he  ? 

14.  21  times  the  number  of  books  in  Henry's  library,  less 
5,  equals  70.     How  many  books  has  he  ? 

15.  James  spent  \  of  his  money  for  a  top,  |  of  it  for  a 
ball,  and  had  10  cents  remaining.  How  much  money  had 
he  at  first  ? 

16.  After  paying  |  and  ]  of  my  debts,  I  still  owed  125. 
How  much  did  I  owe  at  first  ? 

17.  A  merchant  lost  \  of  his  capital,  then  gained  |  as 
much  as  he  had  left,  and  then  had  $10800.  How  much  was 
his  capital  at  first  ? 

18.  Robert's  money,  diminished  by  |  and  4  of  itself,  equals 
$1.25.     How  much  money  has  he  ? 

19.  After  a  fruit  dealer  had  sold  §  of  his  apples,  and  |  of 
the  remainder,  he  had  12  bushels  left.  How  many  bushels 
had  he  at  first  ? 

20.  If  1  of  Wilbur's  money  is  increased  by  \  of  f  of  his 
money,  the  sum  will  be  $54.     How  much  money  has  he? 


234  ANALYSIS 

21.  A  banker  gave  a  f  interest  in  a  bank  to  one  son,  a  \ 
interest  to  another  son,  and  the  remaining  interest,  valued 
at  $10000,  to  his  wife.     What  was  the  value  of  the  bank  ? 

22.  A  lot  was  sold  for  $360,  which  was  f  of  what  it  cost. 
Find  the  cost. 

23.  Mr.  Amos  sold  his  farm  for  $3300,  which  was  §  more 
than  it  cost  him.     Find  the  cost. 

24.  A  typewriter  spends  |  of  his  income  and  saves  $400. 
How  much  is  his  income  ? 

25.  A  suit  of  clothes  was  sold  for  $18,  which  was  \  less 
than  it  cost.     Find  the  cost. 

26.  A  merchant  sold  apples  at  $1.80  a  barrel,  which  was 
•|  more  than  they  cost  him.  How  much  did  they  cost  per 
barrel  ? 

27.  There  are  1200  pupils  in  a  certain  school.  The  num- 
ber of  boys  is  f  of  the  number  of  girls.  How  many  girls  are 
there  in  the  school  ? 

28.  The  united  ages  of  Alice  and  Mary  are  28  years ; 
Alice  is  f  as  old  as  Mary.     How  old  is  Alice  ? 

29.  A  lady  paid  $30  for  a  watch,  which  was  \  more  than 
it  cost.     Find  the  cost. 

30.  A  house  that  cost  $1200  was  sold  for  \  more  than  the 
cost.     How  much  was  gained  ? 

31.  A  has  45  cents,  which  is  |  more  than  B  has.  How 
much  has  B  ? 

32.  How  much  will  a  two-thirds  interest  in  a  store  cost, 
when  a  four-fifths  interest  sells  for  $6000? 

33.  There  are  40  pupils  in  a  school,  and  \  of  them  are 
boys.     How  many  girls  are  there  in  the  school  ? 

34.  If  a  man  owns  §  of  a  mill,  and  sells  §  of  his  interest 
for  $3000,  what  is  the  value  of  the  mill  ? 


THE   EQUATION  235 

35.  A  lady  paid  $35  for  a  cloak.  £  <>f  tin1  cost  of  the 
cloak  was  \  of  what  she  paid  for  other  clothing.  How 
much  did  all  cost? 

36.  A  house  and  lot  cost  $8000.  The  lot  cost  f  as  much 
as  the  house.     How  much  did  the  lot  cost  ? 

37.  A  traveler  went  30  miles  in  two  days ;  the  first  day 
he  went  1^  times  as  far  as  the  second.  How  many  miles 
did  he  travel  the  first  day  ? 

38.  A  sold  a  watch  to  B  for  \  more  than  it  cost  him  ;  B 
sold  it  to  C  for  $20,  thereby  losing  1  of  what  it  cost  him. 
How  much  did  A  pay  for  it  ? 

39.  The  difference  between  two  numbers  is  36,  and  the 
greater  is  three  times  the  less.     What  are  the  numbers  ? 

40.  If  to  |  of  Mr.  Barnhart's  salary  you  add  $40,  the  sum 
will  be  |  of  his  salary.     How  much  is  his  salary  ? 

41.  A  merchant  sold  a  dry  goods  store,  receiving  |  of  the 
price  in  cash.  He  invested  |  of  the  sum  received  in  a  jew- 
elry store  bought  at  $900.  For  how  much  was  the  dry 
goods  store  sold  ? 

42.  What  is  the  value  of  f  of  a  ship  if  |  of  it  is  worth 

$48000? 

43.  A  man  invested  |  of  his  money  in  a  lot.  Had  he  paid 
$100  more  he  would  have  invested  |  of  his  money.  Find 
the  cost  of  the  lot. 

44.  Two  merchants  had  a  profit  of  $9600.  After  paying 
^  of  it  for  rent,  they  divided  the  rest  so  that  one  received  |- 
as  much  as  the  other.     How  much  did  each  receive  ? 

45.  If  Wayne  can  do  a  piece  of  work  in  6  days,  what  part 
of  it  can  he  do  in  1  day  ?  If  Ray  can  do  the  same  work  in 
4  days,  what  part  of  it  can  lie  do  in  1  day? 


236  ANALYSIS 

46.  What  part  can  Ray  and  Wayne  both  do  in  1  day  ? 

47.  If  Ray  and  Wayne  can  do  T5^  of  it  in  1  day,  in  how 
many  days  can  they  do  the  whole  work,  working  together  ? 

48.  If  4  men  can  do  a  piece  of  work  in  3  days,  how  long 
will  it  take  1  man  to  do  it  ? 

49.  If  one  man  can  do  a  piece  of  work  in  12  days,  how 
long  will  it  take  2  men  to  do  it  ? 

50.  If  8  men  can  do  a  piece  of  work  in  2^  days,  how  long 
will  it  take  5  men  to  do  it  ? 

51.  A  jeweler  sold  a  watch  for  $60,  and  gained  |  of  the 
cost.     What  was  the  cost  of  the  watch  ? 

52.  A  horse,  sleigh,  and  harness  cost  $220 ;  the  sleigh  cost 
twice  as  much  as  the  harness,  and  the  horse  cost  4  times  as 
much  as  the  sleigh.     Find  the  cost  of  each. 

53.  Ira  can  do  a  piece  of  work  in  12  days;  Baxter  can  do 
it  in  16  days.  If  Baxter's  wages  are  $1.50  a  day,  how  much 
per  day  should  Ira  receive  ? 

54.  A  man  has  three  houses  which  together  are  worth 
$5700.  The  second  house  is  worth  twice  as  much  as  the 
first,  and  the  third  is  worth  -^  as  much  as  the  other  two. 
How  much  is  the  third  house  worth  ? 

55.  If  A  can  do  a  piece  of  work  in  l-i  days,  B  in  3  days,  and 
C  in  4  days,  in  what  time  can  they  do  it  working  together  ? 

Suggestion.  —  Since  A  does  the  whole  work  in  §  days,  he  does  f  of 
it  in  a  day ;  B  does  i  in  a  day,  and  C  \  in  a  day.  What  part  of  the  work 
do  they  do  together  in  a  day?  How  long,  then,  will  it  take  them  to  do 
the  whole  work  together? 

56.  A  man  bought  three  automobiles.  The  first  cost 
$1500,  the  second  cost  1|  times  as  much  as  the  third,  and 
the  third  cost  twice  as  much  as  the  first.  Find  the  cost  of 
the  second  and  the  third. 


PERCENTAGE 

The  term  per  cent  means  hundredths  or  by  the  hundred. 
The  sign  for  it  is  %. 

Thus,  five  hundredths  may  be  written  1^5,  .05,  5  per  cent,  or  5%. 
These  are  called  equivalents. 

Percentage  is  the  process  of  computing  by  hundredths.  It 
is  simply  an  application  of  decimal  fractions. 

Write  both  as  a  decimal  and  as  a  common  fraction  in  its  low- 
est terms  each  of  the  following  per  cents;  thus,  10%  =  .10  = 


JUL  —    1 

too      iU- 

l.       5% 

5.   371% 

9.   120% 

13.     75% 

2.       6f% 

6.   14|% 

10.   250% 

14.   300% 

3.      81% 

7.   331% 

11.     43% 

15.     ■    1% 

4.    121% 

8.   125% 

12.     65  % 

16.         %  % 

Write  the  following  decimals 

as  fractions  and 

per  cents: 

17.   .05 

21.   .081 

25.    1.50 

29.    .25 

is.   .20 

22.   2.50 

26.    Ill 

30.    .16f 

19.    .331 

23.    1.25 

27.     .031 

31.    .371 

20.   .50 

24.    1.20 

28.    .06f 

32.     .45 

Write  the  following  as  decimals  and  as  per 

cents : 

33.    1 

37.    | 

41      1 
**■■     9 

45      -1- 

12 

34.    \ 

38.     1 

42-    lV 

46.     | 

35.     \ 

39.     \ 

43-  iV 

47.     § 

36.     f 

40.     1 

44.     } 

48.     | 

237 


238 


PERCENTAGE 


Memorize  the  following  equivalents  : 

49.  What  is  50%  of  100  ?  40  ? 
10?  2?  i?  I? 

50.  What  is  16f  %  of  90?  150? 
120?  9?  12?  3? 

51.  What  is  331%  of  3000? 
2000?  50?  75?  100? 

52.  What   is   12|%    0f   200? 
32  ?  96  ?  4  ?  6  ?  1  ? 

53.  Whatis37±%  of  72?  56? 
800  ?  2000  ?  40  ?  8  ? 

54.  What  is  20  %  of  400  ?  600  ? 
l?  i?  16?  20? 


l%  =  iio 

14f%  =  | 

2%  =  51o 

16|%  =  i 

H%  =  £> 

20%    =i 

4%=  A 

25%    =  J 

5%  =  A 

33|%=i 

6i%  =  tV 

37f%  =  | 

6!%  =  iV 

50%    =i 

8J%  =  A 

62J  %  =  | 

n  %  =  it 

66}*-} 

io%=TV 

75%    =| 

in*=* 

8^%  =  f 

12i%  =  l 

871%  =| 

55.    Find  12|%  of  16;  of  48 
800  ;  of  220  ;  of  404. 


of  72;  of  96;  of  168;  of 


56.    Find  5%  of  25;    of  50;    of  75;    of  100;    of  125. 

In  each  example  in  56  we  have  two  terms,  a  per  cent  and  a  number.  In 
each  case  we  are  to  find  5  %  of  the  number.  The  number  of  which  we  take 
the  y|^  (viz.  25,  50,  etc.)  is  called  the  base.  The  number  of  hundredths 
(5)  to  be  taken  is  called  the  rate,  and  the  number  of  hundredths  actually 
taken,  that  is,  the  answer,  is  called  the  percentage. 

The  base  is  the  number  on  which  the  percentage  is 
computed. 

The  rate  or  rate  per  cent  is  the  number  of  hundredths. 
We  generally  express  rate  as  a  decimal. 

The  percentage  is  the  product  obtained  by  taking  a  certain 
per  cent  of  the  base. 

The  sum  or  amount  is  the  base  plus  the  percentage. 

The  difference  is  the  base  minus  the  percentage. 


PERCENTAGE  239 

Finding  a  given  per  cent  of  any  number. 

l.    What  is  20%  of  300?  Think  of  20%  of  300  as  \  of 
300,  or  60. 

Find  : 

2.  2  %  of  100  17.      81  %  of  480 

3.  5  %  of  400  is.      9£  %  of  660 

4.  10%  of  500  19.    111%  of  729 

5.  20%  of  800  20.    121%  of  648 

6.  50%  of  1200  21.    16|%of366 

7.  40%  of  1000  22.    331%  of  333 

8.  25  %  of  360  23.    621  %  0f  864 

9.  30%  of  90  24.  66|%  of  724 
10.  3%  of  420  25.  75%  of  968 
li.      2  %  of  500  26.    871  oj0  of  568 

12.  6%  of  150  27.       6%  of  $60 

13.  7%  of  800  28.       8%  of  $560 

14.  5%  of  440  29.      10%  of  350  acres 

15.  0  %  of  550  30.      30  %  of  960  sheep 

16.  31%  of  900  31.    62i  %  of  856 

Written  Work 

l.    What  is  7  %  of  245  ?  66f  %  of  300  ? 

(a)     245  base  7<>/°  of  a  number  equals  -07  of  ih 

^  J        n„  Therefore,  7%  of  245  is  .07  times  245, 

—M  rate  or  17.15. 
17.15  percentage 

-« n a  662%  0f  a  number  equals  §  of  it. 

(5>     ?  of  £00  =  200  1  of  300  =  200. 


^4.  given  per  cent  of  any  number  is  found  by  multiplying 
the  base  by  the  rate. 


0 

PERCENTAGE 

Find: 

2. 

4%  of  328 

9. 

80%  of  6.75 

3. 

9%  of  1126 

10. 

331%  of  75 

4. 

11%  of  263 

11. 

60  %  of  f 

5. 

15%  of  380 

12. 

14f%  of  105 

6. 

24%  of  165.5 

13. 

75%  of  f 

7. 

38%  of  $77.50 

14. 

87^  oj0  0f  168 

8. 

72  %  of  328 

15. 

331  cj0  of  336 

16.  In  a  school  of  400  pupils,  45  %  are  girls.  How  many 
girls  are  there?    how  many  boys? 

17.  A  clerk  who  received  $50  a  month  had  his  wages 
increased  15%.     How  much  were  his  wages  increased? 

18.  If  iron  ore  yields  63  %  of  pure  metal  to  the  ton,  how 
much  iron  is  there  in  40  tons  of  ore? 

19.  A  merchant,  failing  in  business,  paid  85%  of  his 
debts.     How  much  should  a  creditor  receive  whose  claim  is 

$2850? 

20.  A  bill  of  goods  cost  $137.50.  How  much  was  gained 
by  selling  the  goods  at  a  profit  of  12%  ? 

21.  Compare  48%  of  $45  and  45%  of  $48. 

22.  I  owe  a  debt  of  $246.50.  If  I  pay  40%  of  it  at  one 
time,  and  50%  of  the  remainder  at  another  time,  how  much 
do  I  still  owe  ? 

23.  A  n  automobile  cost  $  3500  and  the  repairs  for  2  years 
were  10%  of  the  cost.  If  the  automobile  was  sold  at  40% 
reduction  from  the  cost,  find  the  entire  loss. 

24.  The  operating  expenses  of  a  factory  are  45  %  of  the 
sales.  If  the  sales  for  a  year  amount  to  $650450,  how  much 
are  the  operating  expenses? 


PERCENTAGE  241 

25.  400  men  were  employed  in  a  factory  at  daily  wages 
averaging  $1.95.  If  100  of  these  men  received  33|  %  of  the 
entire  daily  wages,  rind  their  average  daily  wages.  Find 
the  average  daily  wages  of  the  other  300  men. 

26.  Three  newsboys,  John,  James,  and  Henry  earned  to- 
gether $550  in  a  year.  John  earned  40%,  James  60%  of  the 
remainder,  and  Henry  what  remained.  Find  how  much 
each  earned. 

27.  40%  of  a  Western  farm  containing  600  acres  is  in 
wheat,  30%  of  the  remainder  in  corn,  66|%  of  the  remainder 
in  oats  and  grass.  How  many  acres  are  there  in  each  crop, 
and  how  much  remains  not  cultivated  ? 

Finding  what  per  cent  one  number  is  of  another  number. 
1.    What  part  of  $10  is  $5?     What   %  of  $10  is  $5? 
Think  $5  is  \  of  $10,  or  50%  of  $10. 
What  %  of: 


2. 

20  is  10  ? 

8.    3|  in.  is  1^  in.? 

3. 

35  ft.  is  7  ft.? 

9.    25  gal.  is  64^  gal.? 

4. 

100  is  16|  ? 

10.    60  rods  is  20  rods? 

5. 

500  lb.  is  100  lb.? 

11.      1  mile  is  80  rods? 

6. 

871  is  121? 

12.      1  lb.  (av.)  is  1  oz.  (av.)  ? 

7. 

ij  yd- is  i  ycL? 

13.      1  dollar  is  1  dime  ? 

Written  Work 

l.    What  per  cent  of  75  is  15  ? 

The    unknown    number    is    the    rate. 
15  .j_  75  =  .20  =  20%       Since  the  percentage  equals  the  base  multi- 
plied by  the  rate,  the  rate  must  equal  the 
percentage  divided  by  the  base.     15  divided  by  75  is  .20,  or  20%.     Or,  15 
is  ff,  or  \,  or  20%,  of  75.     Test :  20%  of  75  =  15. 

The  rate  equals  the  percentage  divided  by  the  base. 

BAM.    COMPL.     IR1TH. — 16 


242 


PERCENTAGE 


What  per  cent  of  : 
2.    25  is  10  ? 
32  is  12? 

65  is  39? 

196  is  $72? 


3. 
4. 
5. 
6. 
7. 
8. 
9. 
18 


621  a.  is  6|  A.? 

-2-  is  -&? 

9  i&   9  * 

4isf? 

125  yd.  is  75  yd.? 


10.  4  bu.  is  1  pk.? 

11.  40  is  6§? 

12.  75  is  3.125? 

13.  |  is  .125? 

14.  I|is2i? 

15.  $18  is  $45? 

16.  10  qt,  is  36  qt.? 

17.  $3  is  18  cents? 


Out  of   350  words,  I  spelled  315  correctly.      What 
per  cent  did  I  make  in  spelling? 

19.  From  a  farm  of  160  acres,  24  acres  were  sold.  What 
per  cent  was  sold? 

20.  If  a  man  saves  $262.50  out  of  his  salary  of  $1250, 
what  per  cent  does  he  save  ? 

21.  A  farmer  raised  150  bu.  of  potatoes  from  6  bu.  of 
seed.     What  per  cent  of  the  crop  was  the  seed  ? 

22.  A  merchant  owes  $8750  and  his  assets  are  $3675. 
What  per  cent  of  his  debts  can  he  pay  ? 

23.  A  pupil  misspelled  35  words  out  of  80.  What  per 
cent  did  he  spell  correctly? 

24.  .875  is  what  per  cent  of  .3125? 

25.  I  paid  $5.25  for  the  use  of  $75.  What  per  cent  did  I 
pay? 

26.  A  son,  on  receiving  $5000  from  his  father,  bought  a 
farm  for  $2750,  a  store  for  $1875,  and  deposited  the  rest  in 
a  bank.     What  per  cent  of  his  inheritance  did  he  deposit  ? 

27.  A  house  rents  for  $240  a  year.  The  taxes  and  in- 
surance are  $30.  If  the  property  is  valued  at  $3500,  what  per 
cent  does  the  owner  realize  on  the  value  of  the  property  ? 


PERCENTAGE  243 

Finding  the  number  when  a  per  cent  of  it  is  given. 

1.  If  £  of  a  number  is  10,  what  is  the  number?     If  20% 
of  a  number  is  10,  what  is  the  number  ? 

2.  If  33|  %  of  a  man's  loss  is  $300,  how  much  does  he 
lose? 

3.  If  87 ^  %  of  a  man's  gain  is  $70,  how  much  does  he 
gain  ? 

What  is  the  number  of  which  : 

4.  10  is  66|  %?       li.  40  is  16|  %  ?  18.  $48  is  10  %  ? 

5.  $100  is  331  %  ?  12.  lOt)  is  12.]  rr/0  ?  19.  #12  is  16f  %  ? 

6.  500  is  50  %  ?       13.  300  is  37J  %  ■>  2o.  30  is  331  %  ? 

7.  60  is  75%?         14.  500  is  62^  %?  21.  60  is  66f%? 

8.  $24  is  40  %  ?       15.  700  is  874  %  ?  22.  120  is  20  %  ? 

9.  300  is  60  %  ?       16.   500  is  25  %  ?       23.   $10  is  831  %  ? 
10.   500  is  50  %  ?       17.   600  is  75  %  ?      24.  $50  is  831  <p0  ? 

Written  Work 

1.  Find  the  number  if  33  %  of  it  is  3135. 

(a)    3135  -T-  .33  =  9500  The  unknown  number  is  the  base.    Since 

the  percentage  equals  the  base  multiplied  by 
the  rate,  the  base  equals  the  percentage  divided  by  the  rate,  3125  ■*-  .33  = 
9500,  the  number.    Test :  .33  of  9500  =  3135. 

2.  Find  the  number  if  8|  %  of  it  equals  250. 

si\  Q\tf  _   i  8£%  of  the  number  equals  J2  of  it. 

OK(\    3 12  ~"  Vnnn  H  of  the  number  is  12  x  250>  or  300°- 

zou  x  -r  -  duuu        Test .  A  of  3000  _  250 

The  base  equals  the  percentage  divided  by  the  rate. 


PERCENTAGE 

?in 

d  the  number  if : 

3. 

8%  of  it  is  $2.40             8. 

4. 

12%  of  it  is  $3.60             9. 

5. 

12|%  of  it  is  $91              10. 

6. 

37|%  of  it  is  $27               11. 

7. 

331%  of  it  is  $42.50         12. 

244 


6%  of  it  is  $72 
32%  of  it  is  $3.60 
45%  of  it  is  $3.60 
62-i-%  of  it  is  $35.50 
12.    87|%  of  it  is  $28.28 

13.  A  has  $3612,  which  is  87^%  of  what  B  has.  How 
much  has  B? 

87|%of  B's  =  $3612,  A's. 

14.  If  $14  is  25%  of  A's  salary,  find  his  salary? 

15.  After  a  battle  70  %  of  a  regiment,  or  644  men,  were 
left.     How  many  men  were  there  in  the  regiment  at  first? 

16.  I  drew  from  the  bank  $1500,  or  83±  %  of  my  deposit. 
How  much  was  my  deposit? 

17.  If  a  man  rents  a  house  for  $752  per  year,  which  is 
16%  of  its  value,  what  is  the  value  of  the  house? 

18.  A  teacher's  expenses  are  $30  a  month,  and  this 
amount  is  37|  %  of  his  salary.     How  much  does  he  save? 

19.  The  number  of  pupils  in  attendance  at  school  in  a  cer- 
tain town  is  576,  which  is  96  %  of  the  enrollment.  What  is 
the  enrollment? 

Finding  a  number  when  the  number  plus  the  rate  of  increase 
is  given. 

Written  Work 

1.    What  number  increased  by  17  %  of  itself  equals  585? 

100%  of  itself  =  the  number 

100%  of  itself  +  17%of  itself,  or  117%  of  the  number  =  585,  amount 

1%  of  the  number  =  Tiy  of  585,  or  5 

100%  of  the  number  =  100  X  5,  or  500 

Divide  the  sum  by  one  plus  the  rate. 


PERCENTAGE  245 

What  number  increased  by  : 

2.  8%  of  itself  is  324?  6.  50%  of  itself  is  69? 

3.  30%  of  itself  is  260?  7.  250%  of  itself  is  105? 

4.  37}  %  of  itself  is  550?  8.  16|  %  of  itself  is  1050? 

5.  |  %  of  itself  is  2011?  9.  70%  of  itself  is  510? 

10.  1  gained  35%  by  selling  an  article  for  $4.05.  How 
much  did  it  cost? 

11.  A  laborer  had  his  wages  twice  increased  10%.  If  he 
now  receives  $2.42  a  day,  what  were  his  wages  before  they 
were  increased? 

12.  A  property  sold  for  $4025,  which  was  an  increase  of 
15%  of  the  cost.     How  much  did  the  property  cost? 

13.  A  receives  $1600  salary,  which  is  60%  more  than  B 
receives.     What  salary  does  B  receive? 

14.  W.  H.  Richmond  bought  a  jewelry  store  for  a  certain 
sum  and  increased  the  stock  27  %  of  the  purchase  price.  He 
found  that  the  whole  investment  amounted  to  $5969.  What 
was  the  purchase  price  of  the  store  ? 

15.  The  land  surface  of  the  District  of  Columbia  is  60 
square  miles,  which  is  500  %  more  than  the  water  surface. 
What  is  the  water  surface? 

Finding  a  number  when  the  number  minus  the  rate  of  de- 
crease is  given. 

Writt&a  Work 
1.    What  number  diminished  by  16%  of  itself  equals  168? 

100%  of  the  number  =  the  number 
100%  of  the  number  —  10%  of  the  number, 

or  84  %  of  the  number  =  168  (difference) 

1  %  of  the  number  =  &  of  168,  or  2 

100%  of  the  number,  or  the  number  =  100  x  2,  or  200 

Divide  the  difference  by  one  minus  the  rate. 


246  PERCENTAGE 

What  number  diminished  by : 

2.  45%  of  itself  equals  55?  6.  18f  %  of  itself  equals  325? 

3.  18%  of  itself  equals  246?        7.  23%  of  itself  equals  308? 

4.  621%  (,f  itself  equals  27?        8.  95%  of  itself  equals  25? 

5.  50%  of  itself  equals  22.5?        9.   10%  of  itself  equals  4|  ? 

10.  John  has  $35,  which  is  12|  %  less  than  his  brother  has. 
How  much  has  his  brother? 

11.  Mrs.  Lee  spent  $24  for  a  coat,  which  was  33|  %  less 
than  the  cost  of  a  suit.     Find  the  cost  of  both. 

12.  After  losing  8|%  of  his  money,  a  man  had  $352  left. 
How  much  had  he  at  first? 

13.  What  number  decreased  by  35  %  of  itself  equals  $1300  ? 
$520?     $6500? 

14.  A  school  enrolls  249  boys,  which  is  17  %  less  than  the 
number  of  girls  it  enrolls.  How  many  pupils  are  there  in 
the  school? 

15.  A  lady  when  shopping  spent  $15  of  her  money  for  a 
hat,  which  was  25  %  less  than  the  amount  she  spent  for  a 
coat.     How  much  did  she  spend  for  the  coat  ? 

16.  The  fraction  T9g  is  40  %  less  than  what  fraction  ? 

17.  If  a  certain  number  is  increased  40  %  of  itself,  and 
this  sum  is  diminished  by  50  %  of  itself,  the  result  is  700. 
Find  the  number. 

18.  I  sold  two  lots  for  $1200  each  ;  on  one  T  gained  25% 
and  on  the  other  I  lost  25  % .  Did  I  gain  or  lose  and  how 
much? 

19.  The  population  of  a  town  in  1906  was  14000,  which 
was  121%  less  than  the  population  in  1907.  What  was  the 
population  in  1907? 


REVIEW  OF   PERCENTAGE  247 


REVIEW  OF  PERCENTAGE 


1.  What  is  50%  of  200? 

2.  .05  is  what  per  cent  of  .25? 

3.  .25  is  25%  of  what  number? 

4.  I  sold  goods  for  $8.75.  My  actual  loss  was  $1.25. 
What  was  the  cost  and  the  per  cent  of  loss  ? 

5.  A  man  owns  a  farm  valued  at  $9600.  His  annual 
taxes  are  -$86.40.  How  much  must  he  make  each  year  to 
clear  8  %  on  the  cost  of  his  property  ? 

6.  Ten  is  what  per  cent  of  20?  15  is  150%  of  what 
number  ? 

7.  What  per  cent  of  10  days  are  30  days?  What  per 
cent  of  30  days  are  10  days  ? 

8.  |  of  72  is  how  many  per  cent  of  120  ? 

9.  I  paid  $7200  for  a  house,  $150  for  repairs,  and  $350  for 
delinquent  taxes.  I  then  sold  it  for  $9000.  What  per  cent 
did  1  make  on  my  money  ? 

10.  In  a  business  college  20  %  of  the  students  study  book- 
keeping, 60  %  of  them  study  typewriting,  and  the  remaining 
68  students  study  other  courses.  How  many  students  are 
there  in  the  school  ? 

11.  The  income  from  an  investment  which  pays  5.}%  is 
$220.     What  sum  is  invested  ? 

12.  Mr.  Wilson  buys  a  house  and  lot  for  $6400.  The 
average  expenses  per  year  for  taxes  are  $80;  for  insurance 
$12;  and  for  repairs  $24.  What  must  be  the  annual  rent 
that  he  may  have  an  income  of  6  %  net  on  the  original  cost 
of  the  property? 

13.  What  fraction  increased  by  35%  of  itself  equals  J$? 


248  PERCENTAGE 

14.  If  my  property  sells  for  $7433.25  and  I  owe  $8745, 
what  per  cent  of  my  debts  can  I  pay  ? 

15.  Ten  thousand  boxes  of  fruit  were  sold  for  $9450, 
which  was  33^%  less  than  the  cost.     What  was  the  cost? 

16.  If  12|  %  of  16|  %  of  a  number  is  2J,  what  is  the  whole 
number ? 

17.  A  section  of  land  was  sold  for  $4000,  which  was  25% 
more  than  it  cost.     How  much  did  the  land  cost  per  acre  ? 

18.  Express  as  a  per  cent :  | ;   fa  ;   |. 

19.  A  horse  and  buggy  cost  $300.  If  the  cost  of  the 
horse  was  200%  of  the  cost  of  the  buggy,  what  was  the 
cost  of  each  ? 

20.  After  paying  70  %  of  his  debts,  a  man  found  that  $3600 
would  put  him  out  of  debt.     Find  his  original  indebtedness. 

21.  Thirty-five  per  cent  of  640  pounds  is  5.6%  of  how 
many  tons  ? 

22.  A  bankrupt  sold  his  property  for  $4100,  which  was 
18  %  less  than  its  real  value.  If  the  property  had  sold  for 
$5250,  what  per  cent  above  its  real  value  would  it  have 
brought  ? 

23.  Two  adjacent  properties  sold  for  $13200.  75  %  of  the 
sale  of  one  equaled  90%  of  the  sale  of  the  other.  Find 
the  selling  price  of  each. 

24.  A  certain  excavation  cost  $120.  What  would  be  the 
cost  of  an  excavation  20%  wider?  25%  deeper?  50%  longer? 

25.  What  per  cent  of  121.92  is  15.24  ? 

26.  What  is  the  difference  between  \  %  of  $7000  and  25  % 
of  $7000? 

27.  I  bought  100  bu.  apples  at  50^  a  bushel,  but  lost  20  bu. 
by  freezing.  At  what  price  per  bushel  did  I  sell  the  remain- 
der, if  my  entire  loss  was  4  %  of  the  cost  of  the  apples  ? 


GAIN    AND    LOSS  249 

28.  The  net  profits  of  a  store  in  two  years  were  83483. 
The  profits  the  second  year  were  15%  more  than  the  first 
year.     How  much  were  the  profits  the  first  year  ? 

29.  An  executor  in  settling  an  estate  found  7|  %  uncol- 
lectable,  12^  %  invested  in  city  lots,  40%  in  cash,  15%  loaned, 
and  the  remainder,  810,000,  invested  in  the  home.  The 
estate  was  equally  divided  among  four  sons.  How  much 
did  each  receive  ? 

30.  A  merchant  increased  his  capital  the  first  year  331%, 
and  the  second  year  25  %  of  the  capital  at  the  end  of  the  first 
year.  He  lost  36%  of  his  original  capital  the  third  year, 
and  had  $11760  left.  Was  his  original  capital  increased 
or  decreased,  and  how  much  ? 

31.  An  estate  was  worth  $8400.  Had  it  been  sold  for 
that  amount,  the  creditors  would  have  received  87|  %  of  their 
claims,  but  \  of  the  estate  was  sold  at  18-|  %  below  its  value, 
and  the  remainder  at  12|  %  below  its  value.  What  per  cent 
of  the  debts  did  the  estate  pay? 

GAIN  AND  LOSS 

1.  A  dealer  bought  goods  for  11000,  and  sold  them  at  a 
gain  of  10%.  What  was  the  selling  price?  What  was  the 
gain  ? 

2.  Sugar  that  cost  5P  per  pound  was  sold  at  a  gain  of 
20  % .     What  was  the  gain  per  pound  ? 

3.  A  huckster  bought  fruit  for  820,  but  found  he  had  to 
sell  it  at  a  loss  of  20  %.     How  much  did  he  lose  ? 

4.  A  grocer  sold  butter  that  cost  20^  per  pound,  for 
25  $.     What  part  of  the  cost  did  he  gain  ? 

5.  Books  that  cost  81.50  wholesale  were  sold  at  a  gain 
of  10%.     Find  the  selling  price. 


250  PERCENTAGE 

Gain  and  loss  are  terms  used  to  designate  the  profits  or 
the  losses  in  business  transactions. 

The  cost  is  the  amount  paid  for  an  article ;  the  selling 
price  is  the  amount  received  for  it. 

The  gross  cost  of  goods  is  the  original  cost  increased  by 
what  is  paid  for  freight,  storage,  etc. 

The  net  proceeds  is  the  amount  received  for  goods  after  all 
charges  incident  to  the  sale  have  been  deducted. 

The  per  cent  of  gain  or  loss  is  always  reckoned  on  the  cost  or 
on  the  sum  invested. 

Written  Work 

1.  A  merchant  bought  goods  for  $4500  and  sold  them  at 
a  gain  of  12  %.     How  much  did  he  gain  ? 

Comparative  Study 
$4500,  cost         The  amount  bought  or  sold  corresponds  to  what  term 
.  1 2   rate   *n  fercentctffe  ? 
%  5-1-0  00    m in         ^e  S3*11  or  l°ss  corresponds  to  what  term  in  Per- 
'  °l         centage  ? 

Find  the  gain  or  loss: 

2.  $75,  gain  20%.  6.  $356,  gain  21  %. 

3.  $96,  gain  381%.  7.  $132.50,  gain  28%. 

4.  $115,  loss  15%.  8.  $485.60,  loss  5%. 

5.  $227,  loss  19%.  9.  $880.80,  gain  12 1  %. 

10.  How  much  is  gained  by  selling  a  property  that  cost 
$3250  at  a  profit  of  8%  ? 

11.  A  grocer  bought  120  dozen  eggs  at  18  cents  a  dozen, 
and  sold  them  at  a  profit  of  11^%.     What  was  his  gain? 

12.  A  real  estate  dealer  bought  three  lots  for  $1500,  $1800, 
and  $2000  respectively.  He  sold  the  first  at  an  advance  of 
8%,  the  second  at  an  advance  of  10%,  and  the  third  at  an 
advance  of  12%.     What  was  his  gain  ? 


GAIN    AND   LOSS  251 

Finding  the  gain  or  loss  per  cent. 

Written  Work 

.1.    I  bought  a  piece  of  property  for  $2500  and  sold  it 
for  $2750.     Find  the  gain  or  loss. 

$■2730  -  $2500=  $  250,  gain 
$250  h-  $2500  =  .10,  or  10%,  gain 

Find  the  gain  or  loss  per  cent  when  the  : 

2.  Cost  is  $100  and  the  selling  price  1 105. 

3.  Cost  is  1175  and  the  selling  price  $210. 

4.  Cost  is  $240  and  the  selling  price  $280.40. 

5.  Cost  is  $476.80  and  the  selling  price  $309.92. 

6.  Cost  is  $775.50  and  the  selling  price  $1008.15. 

7.  If  flour  is  bought  for  $4.50  a  barrel  and  sold  for  $6  a 
barrel,  what  per  cent  is  gained  ? 

8.  A  farm  was  bought  for  $3500  and  sold  for  $4200. 
What  was  the  gain  per  cent  ? 

9.  If  hats  are  bought  for  $27  a  dozen  and  retailed  at 
$2.75  each,  what  per  cent  gain  is  realized  ? 

10.  A  grain  dealer  bought  500  bushels  of  wheat  at  84  cents 
a  bushel,  000  bushels  at  80  cents  a  bushel,  and  sold  it  all  at 
82  cents  a  bushel.     What  per  cent  did  he  gain  or  lose  ? 

Finding  the  cost. 

Written  Work 

l.    What  was  the  cost  of  a  house  if  the  owner,  by  selling 
it  at  an  advance  of  25%,  gained  $900? 

$900  =  gain 

$  900  --  .25  =  $3600,  cost 


252  PERCENTAGE 

Find  the  cost  when: 

2.  5%  loss  is  $25.  6.  J%  gain  is  $16.80. 

3.  12±  %  gain  is  $37 J.  7.  44  %  loss  is  $1100. 

4.  150%  gain  is  $750.  8.  35%  gain  is  $12.25. 

5.  I  %  loss  is  $12±.  9.  16|  %  loss  is  $  37.50 

10.  A  dealer  sold  a  buggy  at  25%  gain,  and  received  $90 
for  it.     How  much  did  the  buggy  cost? 

Selling  price  =  £  of  the  cost 
$90  =  |  of  the  cost 
Cost  =  |  of  $90,  or  $72 

Find  the  cost  when  selling  price  at: 

11.  10  %  gain  is  $  220.  14.    37-|  %  loss  is  $600. 

12.  18  %  loss  is  $492.  15.    16|  %  gain  is  $1190. 

13.  121  %  gain  is  $990.  i6.    114%  gain  is  $1284. 

17.  A  merchant,  after  losing  25%  of  his  goods  by  fire, 
had  $8700  remaining.  What  was  the  value  of  his  goods  at 
first? 

18.  An  attorney  turned  over  to  his  client  $1125  after  re- 
taining 10%  for  his  services.  What  amount  of  money  did 
the  attorney  collect? 

19.  If  8%  is  lost  by  selling  an  article  for  $1.15,  how  much 
did  it  cost? 

20.  If  dress  goods  sold  at  $1.50  a  yard  yielded  a  profit  of 
20  %,  how  much  did  the  goods  cost  per  yard? 

21.  Mr.  Rice  sold  his  farm  at  a  gain  of  5  %  and  received 
$  4200  for  it.  What  would  the  gain  per  cent  have  been  had 
he  sold  it  for  $4400? 

$4200  -  1.05  =  $4000,  cost 
$4400  -  $4000  =  $400,  gain 

-  $4000  =  .10,  or  10%,  gain 


REVIEW    PROBLEMS  253 

22.  I  sold  a  horse  for  -1240  and  thereby  lost  20%.  What 
selling  price  would  have  given  me  a  gain  of  20%? 

23.  If  a  merchant  loses  10%  by  selling  goods  at  45  cents 
a  yard,  for  what  should  they  have  been  sold  to  gain  20  %? 

24.  A  piece  of  cloth  was  sold  for  $32,  which  was  at  a  loss 
of  20%.  What  would  have  been  the  loss  percent  had  it 
been  sold  for  $39? 

REVIEW  PROBLEMS 

1.  Find  the  selling  price  of  goods  on  which  there  is  a 
loss  of  2},  %  which  amounts  to  $106.25. 

2.  How  many  per  cent  above  cost  must  an  article  be 
marked  in  order  to  make  25%  after  a  discount  of  20%  has 
been  given? 

3.  I  sold  |  of  an  acre  of  land  for  what  £  of  it  cost. 
What  per  cent  did  I  gain  or  lose? 

4.  At  what  price  must  an  article  that  cost  $60  be  marked, 
so  that  after  deducting  25  %  from  the  marked  price,  a  profit 
of  10%  may  be  realized? 

5.  A  sold  a  property  to  B  and  gained  20  % ;  B  sold  it  to 
C  and  lost  16|  % ;  C  sold  it  to  D  for  $2800  and  gained  12%. 
How  much  did  A  receive  for  the  property? 

6.  Find  the  value  of  a  property  that  increased  annually 
4  %  on  the  previous  year's  value  and  after  three  increases 
was  worth  $11,248.64. 

7.  A  note  was  bought  for  5%  less  than  its  face  and  sold 
for  2%  more  than  its  face.  If  $40.25  was  gained,  what  was 
the  value  of  the  note? 

8.  I  bought  a  lot  for  $1600,  which  was  20%  less  than  its 
real  value,  and  sold  it  for  20%  more  than  its  real  value. 
How  much  did  I  gain? 


254  PERCENTAGE 

9.    If  80%  of  a  car  load  of  wheat  is  sold  for  what  the  car 
load  costs,  what  per  cent  is  gained  ? 

10.  A  company  sells  sewing  machines  to  a  wholesaler  at 
33^%  profit,  the  wholesaler  sells  to  the  retailer  at  12i% 
profit,  and  the  retailer  sells  to  the  trade  at  a  profit  of  20  % . 
Find  the  cost  of  a  machine  to  the  company  when  the  retailer's 
profit  on  the  machine  is  $9. 

11.  A  merchant  marked  his  goods  so  as  to  gain  20  %  ■  By 
giving  credit,  5  %  of  his  sales  were  imcollectable.  His  gain 
was  $1050.     What  was  the  value  of  his  goods? 

12.  A  bankrupt  can  pay  only  80  cents  on  the  dollar. 
What  will  be  the  gain  or  loss  per  cent  to  the  retailer  who 
sold  him  a  buggy  at  30  %  profit  ? 

13.  A  merchant  marked  a  lot  of  goods  costing  $  12.000,  at 
25  %  above  cost,  but  sold  them  at  10  %  less  than  the  marked 
price.     What  per  cent  did  he  gain  ? 

14.  A  merchant  sold  silk  at  45  cents  a  yard  above  cost, 
and  gained  20%.     What  was  the  selling  price  per  yard? 

15.  Mr.  McKay  bought  150  shares  of  W.  Va.  Lumber  Co. 
stock  at  $  140  a  share,  and  200  shares  of  telephone  stock  at 
$120  a  share.  He  sold  the  lumber  stock  at  a  loss  of  10%. 
For  how  much  did  he  sell  the  telephone  stock  per  share, 
if  he  gained  10%  on  the  transaction? 

16.  A  and  B  invested  an  equal  amount  of  money  in  busi- 
ness;  A  gained  $2000  on  his  investment,  and  B  lost  $1500; 
B's  money  was  then  65%  of  A's.  How  much  money  did 
each  invest? 

17.  A  bought  a  horse  and  sold  it  to  B  at  a  gain  of  10%  ; 
B  sold  it  to  C  and  gained  10%.  If  C  paid  131.50  more  for 
the  horse  than  A,  how  much  did  the  horse  cost  A  ? 


COMMISSION  AND  BROKERAGE  255 

COMMISSION  AND  BROKERAGE 

A  person  who  buys  or  sells  goods  or  transacts  business 

for  another  is  called  an  agent,  collector,  commission  merchant, 

or  commission  broker,  according  to  the  nature  of  the  business 

transacted. 

A  commission  merchant  actually  receives  the  goods  which  he  buys 
and  sells  for  another.  A  commission  broker  simply  makes  the  contract 
between  the  buyer  and  the  seller  for  whatever  is  to  be  bought  or  sold, 
the  goods  being  delivered  directly  from  the  seller  to  the  buyer. 

The  commission  or  brokerage  is  a  certain  per  cent  of  the 
amount  of  money  involved  in  the  transaction. 

A  commission  merchant  gets  a  certain  per  cent  on  the 
amount  of  his  sales;  a  collector  gets  a  certain  per  cent  on 
the  amount  collected  ;  a  broker  gets  a  certain  per  cent  of  the 
cost  or  the  selling  price. 

The  net  proceeds  is  the  amount  left  after  commission  and 
all  other  charges  have  been  paid. 

The  one  who  sends  the  merchandise  to  be  sold  is  the  prin- 
cipal, the  shipper,  or  the  consignor. 

Selling  or  collecting  through  an  agent. 

Written  Work 

l.  A  Pittsburg  commission  house  sold  275  barrels  of  apples 
at  $4  per  barrel,  on  a  commission  of  10%.  The  freight 
from  Rochester,  New  York,  was  $67.50  and  the  drayage  was 
$11.25.     Find  the  commission  and  the  net  proceeds  of  the 

sale. 

Amount  of  sale  275  bbl.  at  $  4  $1100.00 

Commission  I0%of  $1100  $110. 

Freight 07.50 

Drayage 11  ■-•"' 

188.75  188.75 

Net  Proceeds $  911-25 


256  PERCENTAGE 

Comparative  Study 

The  amount  bought,  sold,  or  collected  in  Commission  corresponds  to 
what  term  in  Percentage? 

The  rate  in  Commission  corresponds  to  what  term  in  Percentage  ? 

The  commission  or  brokerage  in  Commission  corresponds  to  what 
term  in  Percentage  ? 

The  net  proceeds  in  Commission  correspond  to  what  term  in  Percent- 
age? 

2.  A  real  estate  agent  sold  four  lots  for  $  250,  $  325,  $  395, 
and  $405  respectively.  How  much  was  his  commission  at 
5%? 

3.  A  commission  merchant  sold  320  barrels  of  apples  at 
$3.25  a  barrel  and  16  barrels  of  sweet  potatoes  at  $4.80  a 
barrel.     Find  his  commission  at  7%. 

4.  A  lawyer  collected  an  account  of  $385  for  a  client, 
charging  5%.     How  much  should  he  remit? 

5.  A  cotton  broker  sold  200  bales  of  cotton  of  225  pounds 
each,  at  12 J  ^  per  pound,  charging  a  commission  of  2|  %. 
Find  the  net  proceeds. 

6.  A  lawyer  collects  80  %  of  an  account  of  $  1125.  Find 
his  rate  of  commission  if  he  charges  $  9. 

7.  A  real  estate  agent  sold  475  acres  of  coal  at  $  85  an  acre. 
His  commission  was  $1211.25.     Find  the  per  cent  charged. 

8.  My  agent  bought  180  barrels  of  flour  at  $4.80  per  bar- 
rel. He  paid  $50  freight  and  $6  storage.  I  sent  him 
$  937.28.     What  was  his  rate  of  commission? 

9.  An  attorney  succeeded  in  collecting  90  %  of  the  amount 
of  a  consignment  of  cotton  sold  for  $6700.  He  remitted 
$5874,  retaining  the  balance  to  pay  attorney's  fees  and 
$5.25  freight  charges.  What  per  cent  did  he  charge  for 
collecting? 


COMMISSION    AND   BROKERAGE  257 

10.  My  Chicago  broker  sells  for  me  82560  bushels  of  wheat 
at  83£  ^  per  bushel,  charging  \  #  per  bushel  brokerage. 
Find  the  amount  remitted  to  me. 

Find  the  selling  price  if  a  commission  of: 

li.    2%  =$3.05      14.    41%  =  $56.25    17.  3f  %    =$36.25 

12.  i%=    3.12      15.    ?>{%  =     75.60    18.      1%     =   7.59 

13.  \%=    1.54       16.    1|%=     61.50    19.  4 mills  =  79.00 

20.  An  agent  for  the  Diamond  Pneumatic  Tool  Company 
received  20%  on  the  sales  of  13  pneumatic  drills  averaging 
$737.50  each.  If  his  expenses  for  traveling  and  freight  on 
machines  were  $697.50,  find  his  net  profits. 

21.  James  Amidon  &  Co.  offered  one  of  their  salesmen 
$2400  per  year,  $1800  for  traveling  expenses,  and  2% 
on  all  sales  over  $40000;  or  6%  on  all  sales  if  he  paid  his 
own  expenses.  He  chose  the  former,  and  sold  $72000 
worth  of  goods  in  the  year.  Did  he  gain  or  lose,  and  how 
much,  by  accepting  the  first  offer? 

22.  For  selling  a  house,  a  real  estate  agent  received  $  96. 25, 
which  included  $7.65  for  advertising,  and  $27.90  for  re- 
pairs. Find  the  rate  of  commission,  if  the  house  was  sold 
for  $3035. 

Buying  or  investing  through  an  agent. 

Written  Work 

1.  An  architect  charged  2}2  %  for  plans  and  specifications 
and  2^  %  for  superintending  construction.  His  commission 
amounted  to  $  810.     How  much  did  the  building  cost  ? 

2.  I  telegraphed  my  agent  at  Chicago  to  buy  me  10000 
bushels  of  wheat  at  79  cents  or  less.  lie  bought  at  77| 
cents  and  charged  me  |  cent  per  bushel  brokerage.  Find 
the  amount  of  the  check  I  should  send  him. 

HAM.     COM  PL.     Alt  I'l'll.  —    17 


258 


PERCENTAGE 


3.  An  agent's  investments  in  1905  were  $  80500  and  in  1906 
$  87650.  His  commissions  for  1906  were  $  143  more  than  for 
1905.     Find  his  commission  for  each  year. 

4.  My  broker  in  New  Orleans  buys  50000  pounds  -of  cot- 
ton at  11|^  per  pound.  His  commission  is  |  %  and 
freight,  storage,  and  cartage  amount  to  $  95.80.  How  much 
should  I  remit  ? 

5.  A  house  and  lot  bought  for  $8500  was  sold  afterwards 
for  80  %  of  the  purchase  price.  If  the  agent  received  2% 
on  each  transaction,  find  his  commission. 

6.  An  agent  buys  a  property  for  his  principal  for  $36790 
at  2%  commission.  The  owner  puts  $674.20  in  repairs  and 
afterwards  sells  the  property  through  the  same  agent  for 
$43000,  at  2%  commission.  Find  the  agent's  commission, 
and  the  principal's  rate  per  cent  of  gain. 

7.  An  attorney  invested  for  his  client  $8750  in  a  mort- 
gage. The  owner  of  the  property  paid  the  attorney  2  % 
commission  for  getting  the  money  and  $35.75  for  examining 
title  and  for  docket  fees.  How  much  did  it  cost  the  mort- 
gager to  secure  the  money  ? 

REVIEW 

Find  the  values  of  the  missing  terms  : 


1. 

Gross  Sales 

EXPENSES 

Commission 

Rate  of  Commission 

Net  Proceeds 

$675 

$11.25 

(           ) 

8% 

(           ) 

2. 

$550 

$4.00 

$22.00 

(        ) 

(           ) 

3. 

(         ) 

$119.00 

(         ) 

20% 

$681 

4. 

$560 

00 

$56.00 

(        ) 

(        ) 

5. 

(        ) 

00 

$48.00 

(        ) 

$552 

6. 

$1000 

00 

(        ) 

4% 

(         ) 

7. 

(    ) 

(         ) 

$134.00 

2% 

$6566 

8. 

$2500 

$46.00 

$50.00 

(        ) 

(         ) 

INSURANCE  259 

9.  A  fruit  grower  ships  to  his  commission  merchant  600 
barrels  of  apples,  which  are  sold  at  $  3.50  per  barrel.  The 
agent  deducts  143.90  freight  charges,  $27.75  cartage,  12  ^ 
per  barrel  for  cold  storage,  and  5  %  commission.  Find  the 
amount  remitted. 

10.  My  agent  sends  me  a  bill  for  $37800,  which  includes 
the  cost  of  some  land  bought  at  $100  an  acre  and  his  com- 
mission of  5%.     Find  the  number  of  acres  purchased. 

11.  My  purchasing  agent  in  Chicago  sends  me  a  bill  for 
$6776.60,  covering  cost  of  mining  machinery,  commission  of 
2%,  and  $65  for  extra  expenses.  Find  his  commission  and 
the  cost  of  the  machinery. 

12.  My  agent  retains  %\°fo  commission,  pays  freight 
charges  of  $16.80,  storage  and  drayage  of  $9.75,  and  remits 
to  me  $1594.65.     Find  the  amount  of  gross  sales. 

13.  An  investment  broker  in  Denver  receives  a  draft  for 
$  23935.  This  includes  a  commission  of  2  %  for  investing, 
and  an  allowance  of  $  175  for  traveling  expenses.  Find  the 
amount  invested. 

INSURANCE 

Insurance  is  security  against  loss  or  damage. 

A  merchant  owns  a  store,  uninsured,  valued  at  $  5000.  If  it  is  burned, 
who  will  bear  the  loss  ?  An  insurance  company  agrees  to  insure  the  store 
for  $4000  at  1  %  annually.  In  case  the  store  is  totally  destroyed  by  fire, 
how  much  is  the  company  expected  to  pay  to  the  merchant?  How  much 
must  the  merchant  pay  annually  to  the  company  to  guarantee  this  loss? 

The  policy  is  a  written  contract  between  the  person  insured 
and  the  insurance  company. 

The  premium  is  the  sum  paid  for  the  insurance. 

The  rate  is  a  specified  number  of  cents  or  dollars  per  $100 
of  insurance,  or  a  certain  per  cent  of  the  sum  insured. 

The  term  is  usually  a  year  or  a  period  of  years.  Short 
rates  arc  rates  charged  when  the  term  is  less  than  one  year. 


ofjO  PERCENTAGE 

Property  Insurance 

The  principal  kinds  of  property  insurance  are  fire  insur- 
ance and  marine  insurance.  Other  forms  are  burglar  insur- 
ance, insurance  against  bad  debts,  etc. 

l.  A  frame  dwelling  with  a  tin  roof  is  insured  for  $2800 
for  one  year  at  1  %.     Find  the  premium. 

Written  Work 
Comparative  Study 

The  amount  insured  corresponds  to  what 
$2800,  amount  insured     term  in  Percentage  ? 

^-.         ,  The  rate  corresponds  to  what  term  in 

'      '  Perppntfuip  ? 


Percentage  t 


$28.00,  premium  -pjie  premium  corresponds  to  what  term 

in  Percentage  f 

2.  A  brick  house  is  insured  for  ¥4000  at  60^  on  the  $100. 
Find  the  rate  of  premium  and  the  annual  premium. 

3.  If  the  three-year  rate  is  twice  the  rate  for  one  year,  find 
the  cost  of  insuring  a  brick  dwelling  for  $6500  for  3  years 
when  the  annual  rate  is  45^  per  $100. 

4.  A  store  building  is  insured  for  $8500  and  the  annual 
premium  is  $212.50.  Find  the  rate  per  cent  of  premium 
and  the  annual  cost  per  $100  of  insurance. 

5.  A  school  board  pays  annually  $45  for  $6000  of  fire  pro- 
tection on  a  school  building.     Find  the  rate  of  premium. 

6.  The  premium  on  a  dwelling  insured  for  $5500  is  $38.50 
for  three  years.     Find  the  average  rate  for  a  year. 

7.  If  the  premium  on  a  plate-glass  policy  is  $9.50  and  the 
rate  is  |%,  rind  the  face  of  the  policy. 

8.  Mr.  Lawrence  wrote  a  check  for  $31.50  to  pay  the  in- 
surance on  his  dwelling  for  3  years.  If  the  house  cost  $2400 
and  was  insured  for  I  of  its  value,  rind  the  rate  for  the  term. 


INSURANCE  Jtil 

9.  A  farmer  insured  his  house  for $2700  at  1]%.  his  bam 
for  $1200  at  \%,  and  his  furniture  for  $900  at  1%.  What 
premium  did  he  pay  ? 

10.  A  drug  store  is  insured  for  |  of  its  value  at  2%. 
What  is  the  value  of  the  store  if  the  premium  is  #192  ? 

11.  The  premium  on  8000  bushels  of  wheat,  valued  at  90^ 
per  bushel  and  insured  at  \  of  its  value,  is  $57.60.  Find  the 
rate  of  insurance. 

12.  A  jewelry  store  is  insured  for  $20000  and  its  con- 
tents for  $27000.  The  premium  is  $705.  What  is  the  rate 
of  insurance  ? 

13.  A  clothier  insured  his  stock  of  goods,  valued  at 
$12000,  for  1  year  at  1|%.  At  the  end  of  6  months  he 
surrendered  his  policy.  If  the  "  short  rate  "  for  G  months 
was  90^  per  $100,  how  much  premium  was  returned? 

14.  A  farmer  insured  his  buildings  for  $3500  at  \\%  for 
a  term  of  3  years.  After  he  had  paid  the  premium  for  4 
terms  the  buildings  were  totally  destroyed  by  fire.  What 
was  the  farmer's  loss  ?   the  company's  loss  ? 

15.  A  vessel  worth  $27000  is  insured  for  §  of  its  value 
at  3|%.  In  case  of  shipwreck,  what  is  the  company's  loss  ? 
What  is  the  owner's  loss  ? 

16.  How  much  insurance,  at  |%,  can  be  placed  on  a  build- 
ing for  $42  ? 

17.  A  business  block  valued  at  $300000  was  insured  in 
4  different  companies,  the  rate  of  each  being  1%.  The 
first  company  took  $50000  ;  the  second,  $60000  ;  the  third, 
$90000  ;  and  the  fourth  the  remainder.  After  the  premiums 
had  been  paid  four  times,  the  block  was  damaged  by  fire  to 
the  amount  of  $120000.  What  was  the  loss  of  each  com- 
pany ? 


262 


PERCENTAGE 


Personal  Insurance 

The  principal  kinds  of  personal  insurance  are  life  insurance 
and  accident  insurance. 

Kinds  of  life  insurance  policies : 

1.  A  life  policy  is  one  that  guarantees  a  fixed  sum  of  money  on  the 
death  of  the  insured.     The  premiums  on  a  life  policy  run  for  life. 

2.  A  life  policy  with  a  twenty-year  settlement  is  one  that  guarantees, 
after  twenty  annual  payments  have  been  made,  either  a  cash  surrender 
value,  or  a  paid-up  policy,  payable  at  death. 

3.  An  endowment  policy  is  one  in  which  the  face  of  the  policy  and 
the  profits  on  the  premiums  are  guaranteed  to  the  insured  if  living  at 
the  end  of  a  specified  time,  or  to  his  estate  if  his  death  occurs  within  the 
time. 

4.  A  term  policy  is  one  in  which  the  face  of  the  policy  is  paid,  provid- 
ing the  insured  dies  within  the  time  the  policy  runs.  Otherwise  nothing 
is  paid. 

Most  insurance  companies  pay  dividends  on  the  premiums  already  paid, 
thus  lessening  the  amount  of  the  annual  premium. 

The  premium  is  always  so  much  on  $  1000  of  insurance;  thus,  a 
premium  of  f  23.40  means  $23.40  on  $1000. 

The  age  of  the  insured  is  always  reckoned  according  to  the  age  at  his 
nearest  birthday. 

This  table  shows  the  annual  premiums  for  each  $  1000  insurance  in  a 
leading  insurance  company. 


Age 

Ordinary  Life 

20-Payment  Life 

•20-Year  Endowment 

•20-Year  Term 

20 

$18.95 

$27.64 

$49.35 

$  12.48 

25 

21.14 

30.05 

45.98 

13.34 

30 

23.96 

32.98 

50.74 

14.61 

35 

27.63 

36.62 

51.88 

16.70 

40 

32.48 

41.18 

53.69 

20.15 

45 

39.02 

47.09 

56.70 

25.85 

50 

47.79 

54.98 

61.75 

35.00 

55 

60.33 

65.81 

70.02 

60 

77.48 

81.09 

INSURANCE  263 

Dividends  vary  according  to  the  number  of  premiums  that  have  been 
paid.  It  is  fair  to  estimate  that  the  dividends  on  an  ordinary  life  policy 
after  20  annual  premiums  have  been  paid,  will  amount  to  about  25%  of 
the  sum  of  the  annual  premiums. 

Written  Work 

Rates  as  given  in  the  table  on  page  262. 

1.  What  is  the  premium  on  an  ordinary  life  policy  of 
$5000  at  the  age  of  30? 

2.  A  man  at  the  age  of  25  takes  out  a  $  2000  ordinary  life 
policy.  If  he  dies  after  paying  16  premiums,  what  per  cent 
of  the  face  of  the  policy  has  been  paid  in  premiums  ? 

3.  If,  in  example  2,  the  insured  had  taken  a  20-payment 
life  policy,  what  per  cent  of  the  face  of  the  policy  would 
have  been  paid  in  premiums  ? 

4.  A  young  man  at  the  age  of  20  took  out  a  20-payment 
life  policy  for  12000.  The  dividends  at  the  end  of  20  years 
amounted  to  $142  per  thousand.  What  was  the  net  cost  of 
this  insurance  at  the  expiration  of  this  policy,  if  the  interest 
on  the  premiums  is  not  considered  ? 

5.  What  is  the  premium  on  a  20-year  endowment  policy 
for  $5000  at  the  age  of  40  ? 

6.  The  first  annual  premium  on  a  20-year  endowment 
policy  for  $8000  amounts  to  $453.60.  What  is  the  age  of 
the  insured  ? 

7.  If  a  man  25  years  old  takes  out  a  20-term  policy  for 
$  3000,  how  much  will  he  have  paid  for  his  insurance  at  the 
close  of  the  term  ? 

8.  A  man  at  the  age  of  25  took  out  a  20-payment  life 
policy  for  $1000.  His  dividends  for  the  20  years  amounted 
to  $150.45.  What  was  the  amount  of  his  premiums,  less  the 
dividend? 


264  PERCENTAGE 

COMMERCIAL   DISCOUNT 

1.  I  owe  a  bill  of  $50  clue  in  60  days.  As  the  creditor 
needs  the  money  he  offers  to  take  $40  if  I  pay  at  once.  What 
per  cent  is  the  reduction  ?    On  what  is  the  reduction  reckoned  ? 

2.  A  catalogue  lists  goods  at  11.00,  -$.50,  $.25,  subject  to 
a  discount  of  20  %.     Find  the  net  price  of  each  article. 

3.  In  the  above  examples  what  numbers  correspond  to  the 
base  in  Percentage  ? 

The  fixed  or  list  price  of  an  article  or  the  amount  of  an 
obligation  is  always  considered  the  base. 

Commercial  discount  is  a  reduction  from  the  fixed  or  list 
price  of  an  article,  or  from  the  amount  of  a  bill  or  obligation. 

1.  Trade  discounts  are  reductions  from  the  fixed  or  list  price  of  an 
article  at  the  time  of  sale. 

2.  Time  discounts  are  reductions  from  a  bill  or  other  obligation  for 
payment  within  a  certain  time. 

3.  Cash  discounts  are  reductions  made  for  the  immediate  payment  of 
a  bill  of  goods  sold  on  time. 

The  net  price  is  the  price  after  trade  discounts  have  been  deducted. 

Written  Work 

1.  Neckties  listed  at  $6.00  per  dozen  are  sold  at  50  %  dis- 
count.    Find  the  net  price.     What  is  the  kind  of  discount  ? 

2.  An  agent  buys  $100  worth  of  goods  on  60  days'  time, 
or  5%  off,  if  paid  immediately.  What  kind  of  discounts  is 
he  offered  ? 

3.  A  merchant  offers  $100  worth  of  goods  for  $90.  What 
is  the  kind  of  discount  ?     What  is  the  per  cent  of  discount  ? 

4.  I  pay  cash  for  a  bill  of  goods  sold  on  60  days'  time,  and 
thereby  get  10%  discount,  or  $12.50.  Find  the  amount  of 
the  purchase.      Why  is  this  a  cash  discount  ? 


COMMERCIAL   DISCOUNT  265 

5.  A  suit  marked  $40  is  offered  for  $28.  Find  the  per 
cent  of  discount.     What  is  the  kind  of  discount  ? 

6.  A  merchant  buys  boys'  suits  at  $60  per  dozen  list 
price,  less  20  %.     What  is  the  kind  of  discount  ? 

7.  A  dealer  sells  $75  worth  of  goods  at  5  %  discount,  if  paid 
within  60  days,  or  10  %,  if  paid  in  cash.  Explain  the  different 
kinds  of  discount,  and  the  amount  saved  by  paying  cash. 

8.  Why  does  a  cash  discount  always  cut  out  a  time  dis- 
count ?     What  discount  is  made  without  reference  to  time  ? 

Business  houses  print  on  their  billheads  their  terms  of 
credit.     For  example: 

1.  "Terms:  60  days  net;  3%  off  10  da," 

2.  "Terms:   00  days  net;   60  days  2%;    10days5%." 

3.  "Terms:  30  days  net ;  cash  5%,  etc." 

9.  Johnston  Bros.,  Toledo,  O.,  purchase  of  Amidon  &  Co., 
Chicago,  $300  worth  of  merchandise.  Terms:  60  da.  net; 
5%  off  10  da.       Find  the  discount  if  paid  within  10  days. 

10.  I  buy  $600  worth  of  goods.  Terms:  30  da.  net; 
5  %  off  for  cash.     Find  the  amount  I  save  by  paying  cash. 

11.  Explain  the  meaning  of  a  bill  head  which  reads  as 
follows:     "Terms:    60da.net;    10%  cash." 

12.  $200  worth  of  goods  are  bought  Aug.  10, 1905.  Terms: 
60  da.  net ;  5  %  off  30  da. ;  10  %  off  10  da.  Find  the  amount 
saved  by  payment  Sept,  5. 

13.  Jamison  &  Son,  Baltimore,  Md.,  bought  $1500  worth 
of  merchandise  from  Brown  &  Co.,  Philadelphia.      Terms: 
90  days  net;   2%  off  60  da.;  5%  off  30  da.;   10%  off  cash.. 
What  was  the  amount  of  the  bill  if  cash  was  paid  ? 

14.  Which  is  the  best  discount  on  a  bill  of  goods  for  $200 
and  how  much:  10%  for  cash,  5%  for  60  days,  or  2%  for 
90  days?     Explain  why. 


266  PERCENTAGE 

Successive  Trade  Discounts 

Wholesale  merchants,  publishers,  and  manufacturers 
usually  have  fixed  price  lists  for  their  goods  from  which  the 
retailer  gets  a  certain  trade  discount.  If  a  reduction  from 
these  prices  is  to  be  made,  an  extra  discount  is  taken  from 
the  former  discount  price. 

1.  A  music  dealer  buys  an  organ  on  60  days'  time,  list 
price  $100  at  40  %,  20  %  off.     Find  the  net  price. 

.40  X  $100=  $40,  1st  discount  Observe    that,    when 

$100  -  $40  =  $60, 1st  discount  price  more  than  one  discount 

-.„.  ,»..«   rti   t  is     given,     each   succes- 

.20x$60  =$12, 2d  discount  .    *       '      .        ,       , 

'    "  ^  w  v      '  sive  discount  is  reckoned 

$60    -$12    =$48,  net  COSt  on  the  last  discount  price. 

2.  Providing  the  music  dealer  gets  a  further  discount  of 
10  %  for  cash,  find  the  price  of  the  organ. 

3.  On    what    discount    price    was     the     last     discount 

reckoned? 

NOTE.  —  The  trade  discount  is  first  deducted ;  then  the  cash  discount 
is  taken  from  the  remainder. 

Find  the  net  cost  of  articles  listed  at : 

4.  $90,  discount  30%,  10%. 

5.  $120,  discount  25  %,  20%. 

6.  $240,  discount  10%,  331%. 

7.  $  35,  discount  20  % ,  5  % . 

8.  $12.50,  discount  20%,  20%. 

9.  $348,  discount  20%,  10%,  5%. 

10.  $100,  discount  10  %,  5  %,  2  %. 

11.  $425,  discount  37^%,  16%. 

12.  $400,  discount  20%,  10%,  5%. 

13.    What  is  the  net  price  of   a  bill  of  goods  for  $5700 
after  discounts  of  25  %,  20  %,  and  5  %  are  allowed  ? 


COMMERCIAL   DISCOUNT  26 


>i 


14.  The  amount  of  discounts  at  20%,  5%  off,  is  $42. 
What  is  the  list  price  of  the  bill  ? 

Suggestiox.  —  The  total  discount  expressed  in  per  cent  is  20%+  (5% 
of  80%),or  24 %.     $42  is  24 %  of  what  number  ? 

15.  What  is  the  cost  of  a  bill  of  farming  implements 
listed  at  $480,  discounts  50%,  5%,  and  freight  $3.60  ? 

16.  Goods  marked  $50  were  bought  at  10  %  trade  discount, 
2%  off  for  cash.     If  sold  at  $55,  what  was  the  rate  of  gain  ? 

17.  A  dealer  bought  50  gross  of  buttons  for  25%,  10  %? 
5%  off  and  sold  them  for  $35.91,  making  a  profit  of  12%. 
What  was  the  list  price  of  the  buttons  per  gross  ? 

18.  A  grocer  is  offered  a  discount  of  10  %  from  one  firm 
on  a  bill  of  goods  of  $1000,  and  two  successive  discounts  of 
5  %  by  another  firm  on  the  same  bill.  Which  is  the  better 
offer  and  how  much  ? 

19.  What  is  the  difference  between  a  discount  of  15  %,  5  %, 
on  a  bill  of  $2000  and  a  discount  of  5  %,  15%,  on  the  same 
bill  ?  Show  that  the  same  result  is  obtained  from  any  num- 
ber of  discounts  on  a  bill  in  whatever  order  they  are  taken. 

20.  Three  firms  bid  on  the  glass  for  a  building  as  follows  : 
(1)  $2000,  00%,  20%,  off.     (2)  $2100,  70%,  10%.  off. 

(3)  $2400,  80%,   10%,  off.      Which  offer  is  the  best  and 
how  much  ? 

21.  A  jobber  buys  merchandise  listed  at  $1500,  at  20%, 
15  %  off,  and  sells  at  15  %,  1 0  %,  5  %  off  the  list  price.  Find 
his  profits. 

22.  I  purchased  $2000  worth  of  goods  trade  discount 
20%,  cash  5%.  I  pay  cash  plus  $5.95  freight.  What  is 
the  entire  cost  of  the  goods  ? 

23.  Find  a  single  discount  equal  to  successive  discounts 
of  40%,  20%,  10%. 


268 


PERCENTAGE 


COMMERCIAL   BILLS 

1.  On  June  10,  1906,  James  Boydson,  Sandusky,  O., 
bought  of  J.  M.  Gordon  &  Co.,  Cleveland,  O.,  35  dozen 
bronze  locks  at  $5.50  per  dozen,  less  20  %,  10%.  Terms: 
30  days  net;  5%  off  10  days. 

Form  of  Bill 


Cleveland.  O.,  fane  /O,  /<?06. 

Bou<$r;t  of  J.  M.  GORDON  &  CO., 

Hardware  Merchants 
Terms  :  30  cla,y&  net ;    5 °Jo  o-f^  /O  cLx^i^. 

Re* 

,&iA>-&C 

35  J&oa.  fduyyvit,  Lo-@£&  @$5.  60 

X&o-a*  5/  to 

&aoA,  t&QA>  5% 
f.  711.  gcyutcni  V  &0-. 

53 

50 
<?0 
60 

$3 

f/31 

67 

138 
6 

In  the  above  problem  J.  M.  Gordon  &  Co.  received  payment  within 
10  days,  so  a  cash  discount  of  5  %  was  deducted  from  the  $  138.60,  making 
the  payment  1131.67.  Had  the  bill  not  been  paid  for  30  days,  the  net 
amount  would  have  been  $  138.60. 

2.  Harmon  &  Co.,  Seattle,  Wash.,  order  from  Peabody  & 
Sons,  Chicago,  111.,  10  doz.  Acme  lawn  mowers,  list  $10  each 
less  40  %,  20%.  Terms:  60  days  net;  5%  off  10  days. 
Make  out  receipted  bill  if  paid  in  10  days. 


LOCAL   AND   STATE   TAXES  260 

3.  Howard  Johnston,  Johnstown,  N.Y.,  orders  from  the 
Acme  Buggy  Co.,  Cincinnati,  O.,  12  buggies,  list  1100,  less 
40  %,  20  %.  Terms  :  30  days  net ;  2  %  off  in  10  days.  Make 
out  receipted  bill  if  paid  in  10  days. 

4.  Fisher  Bros.,  Hagerstown,  Md.,  order  from  the  Fulton 
Hardware  Co., New  York, N.Y., the  following;  discount  33^%: 

1  Gas  Range  @  8  32.00 

100  ft.  Hose  @         .15 

24  Garden  Rakes  @         .50 

Terms :  30  days  net ;  2  %  off  in  10  days.     Make  out  receipted 
bill  if  paid  in  30  days. 

LOCAL  AND  STATE  TAXES 

A  tax  is  a  sum  of  money  levied  on  a  person,  his  prop- 
erty, or  business  for  public  purposes. 

Cities,  towns,  townships,  and  counties  levy  and  collect  taxes  annually 
on  all  taxable  property.  States  ordinarily  levy  taxes  only  on  special 
kinds  of  property. 

A  poll  tax  is  a  tax  levied  upon  male  citizens  over  21  years 
of  age  without  regard  to  the  property  they  own. 

Real  property,  or  real  estate,  is  any  fixed  property  ;  as  land 
and  buildings  erected  thereon. 

Personal  property  is  any  movable  property  ;  as  money, 
stocks,  furniture,  etc. 

An  assessor  is  a  person  elected  or  appointed  to  estimate 
the  value  of  property  to  be  taxed. 

The  rate  of  taxation  is  a  certain  number  of  mills  on  each 
dollar  of  assessed  valuation,  or  a  number  of  cents  on  a  hun- 
dred dollars  of  assessed  valuation.  Thus,  a  tax  levy  of  2 
mills  on  the  dollar,  means  2  mills  (or  t2q%)  on  each  dollar. 

A  collector  is  a  person  elected  or  appointed  to  collect  the 
tax.      He  receives  either  a  salary  or  a  commission. 


270  PERCENTAGE 

I.  Find  my  taxes  on  property  assessed  at  $5000  on  which 
I  pay  5  mills  on  the  dollar. 

Find  the  tax  on  property  assessed  at  : 

2.  $2000,  tax  levy  3  mills.         6.  $3200,  tax  levy  2|  mills. 

3.  $3000,  tax  levy  5  mills.         7.  $5000,  tax  levy  3|  mills. 

4.  $5000,  tax  levy  12  mills.       8.  $12000,  tax  levy  5|  mills. 

5.  $8000,  tax  levy  11  mills.       9.  $20000,  tax  levy    J  mill. 

How  many  mills  on  the  dollar  is  paid  if  the  assessment  is : 
10.    $6000,  taxes  $60?  14.    $600,    taxes  $7.20? 

II.  $1200,  taxes  $24?  15.    $1000,  taxes  $45? 

12.  $8000,  taxes  $32?  16.    $5000,  taxes  $10? 

13.  $  6000,  taxes  $  3  ?  17.    $  950,    taxes  $1.90? 

Find  the  assessed  valuation  if  the  taxes  are  : 

18.  $4.00,    rate    8  mills.  22.    $60,    rate    3  mills. 

19.  $12.00,  rate  12  mills.  23.    $200,  rate  10  mills. 

20.  $6.50,    rate  13  mills.  24.    $180,  rate    6  mills. 

21.  $20,       rate    4  mills.  25.    $200,  rate  25  mills. 

Written  Work 

1.  A  town  whose  property  is  assessed  at  $1750000  needs 
$5150  for  improvements;  there  are  620  persons  who  pay  a 
poll  tax  of  $1.25  each.  What  is  the  rate  of  taxation,  and 
what  is  Mr.  Randolph's  tax,  whose  property  is  valued  at 
$6500  and  who  pays  his  own  and  one  other  poll  tax? 

620  x  $  1.25        =  $775,  the  amount  of  poll  tax. 
$5150  -  $775         =  $4375,  the  amount  of  property  tax. 
$4375  --  $1750000  =  .0025,  the  rate  of  taxation. 
.0025  x  $6500        =  $16.25,  Mr.  Randolph's  property  tax. 
2  x  $1.25        =  $   2.50,  Mr.  Randolph's  poll  tax. 
$16.25  +  $2.50-       =  $18.75,  Mr.  Randolph's  entire  tax. 


LOCAL    AND   STATE   TAXES 


271 


Comparative  Study 

The  assessed  valuation  corresponds  to  what  term  in  Percentage  t 

Tax  corresponds  to  what  term  in  Percentage  f 

The  rate  of  taxation  corresponds  to  what  term  in  Percentage  f 

Find  the  missing  terms : 


Estimated 
Valuation 

ASSESSED 

Valuation 

Rate 

Taxes 

Poll  Tax 

2. 

$ 23000 

$19000 

.002 

(                 ) 

3  polls,  $1  each 

3. 

$147500 

80% 

.002 

(            ) 

2  polls,  $2  each 

4. 

$  120000 

$95000 

(  ) 

$332.50 

5. 

125% 

(           ) 

.015 

11.25 

6. 

150% 

(           ) 

.022 

$3269.20 

7.  The  assessed  valuation  of  a  town  is  $  900000  and  the 
amount  of  taxes  to  be  raised  is  $  16200.  What  is  the  rate  of 
taxation  and  what  is  Mr.  Owen's  tax  who  owns  property 
assessed  at  $  10000  and  personal  property  assessed  at  $2500? 

8.  How  much  tax  does  a  farmer  pay  who  owns  80  acres 
of  land  valued  at  $  100  an  acre,  assessed  at  §  of  its  value,  and 
personal  property  assessed  at  11250,  if  the  rate  of  taxation  is 

three  mills? 

9.  Mr.  Day's  city  tax,  at  the  rate  of  13  mills  on  the  dollar, 
is  $84.50.  What  is  the  estimated  value  of  his  property,  if 
it  is  assessed  at  i  of  its  value  ? 

10.  A  collector  paid  to  the  borough  authorities  821898.50 
after  deducting  his  commission  of  2k%  for  collecting.  What 
was  the  amount  of  taxes  collected,  and  what  were  the  collec- 
tion fees? 

Si  <;t;i  stion.  —The  proceeds  of  each  dollar  returned  by  the  collector 
was  $.97£. 


272  PERCENTAGE 

11.  The  real  estate  of  a  town  is  valued  at  $985470  and 
the  personal  property  at  $195645.  A  tax  of  $7866.69  is 
to  be  raised.  There  are  780  persons,  each  assessed  a  poll 
tax  of  $1.  How  much  tax  will  Mr.  Cowperthwait,  a  non- 
resident (paying  no  poll  tax),  pay  whose  property  is  assessed 
at  $12460? 

12.  Mr.  Arbuthnot's  property  has  an  actual  valuation  of 
$4800.  If  he  pays  17  mills  city  tax  and  3|  mills  county  tax 
on  a  |  valuation,  in  a  certain  year,  find  the  amount  of  his  tax 
for  that  vear. 

13.  A  borough  bridge  cost  $4380.48.  It  was  paid  by  a 
tax  on  the  assessed  valuation  of  the  borough  property.  If 
4%  of  the  tax  was  uncollectable,  and  the  collector's  fee  was 
2|%,  what  was  the  borough  assessment? 

14.  A  tax  collector's  report  in  a  certain  city,  for  Oct.  2,1906, 
showed  by  the  assessment  in  the  tax  book  that  $22742.90 
was  collected  during  September.  If  5  %  discount  was  allowed 
on  each  one's  taxes  paid,  and  the  collector's  commission  was 
2  %,  find  the  amount  paid  to  the  school  treasurer. 

DUTIES  OR  CUSTOMS 

The  revenues  of  our  national  government  are  of  two 
kinds  :  internal  revenues  and  custom  revenues,  or  duties. 

Internal  revenue  is  a  tax  on  the  manufacture  or  sale  of 
malt  liquors,  tobacco,  etc. 

Custom  revenues,  or  duties,  are  taxes  on  goods  imported 
from  foreign  countries.  These  are  collected  at  the  custom- 
houses, which  are  maintained  by  the  government  at  various 
ports  of  entry. 

A  tariff  is  a  schedule  of  duties  on  imports  fixed  by  our 
government. 


DUTIES   OR   CUSTOMS  273 

All  merchandise  brought  into  our  country  is  classified  as 
follows  : 

(1)  Merchandise  on  the  free  list,  that  is,  free  of  duty. 

(2)  Merchandise  subject  to  an  ad  valorem  duty,  that  is,  a 
certain  per  cent  of  the  cost  of  the  goods,  as  shown  by  the 
invoice. 

Invoices  are  statements  showing  the  market  price  of  goods,  expressed 
in  the  money  of  the  country  where  the  goods  are  bought. 

(3)  Merchandise  subject  to  a  specific  duty,  that  is  to  a 
certain  amount  per  yard,  pound,  bushel,  etc.,  without  regard 
to  value. 

(4)  Merchandise  subject  to  both  an  ad  valorem  and  a 
specific  duty. 

For  example,  the  duty  on  Brussels  carpet  is  28 j*  per  square  yard 
specific  and  40%  ad  valorem. 

Duties  are  not  computed  on  parts  of  a  dollar.  If  the  invoice  shows 
a  number  of  cents  less  than  50,  they  are  rejected  in  computation  of 
duties.     More  than  50  cents  are  counted  as  another  dollar. 

Tare  is  an  allowance  made  for  the  weight  of  the  boxes  or  bags 
used  in  packing.     It  is  deducted  before  computing  duties. 

Comparative  Study 

The  cost  of  imported  goods  corresponds  to  what  term  in  Percentage  ? 
The  rate  in  duties  corresponds  to  what  term  in  Percentage  f 
The  duty  corresponds  to  what  term  in  Percentage  ? 

Written  Work 
Find  the  duty  on  the  following  imports : 

1.  1650  lb.  of  hops,  specific  duty  12  ^  per  pound. 

2.  $6250  worth  of  clocks  at  40  %  ad  valorem. 

3.  $  10000  worth  of  uncut  diamonds,  ad  valorem  duty 
60%. 

4.  2400  pounds  of  butter  at  0  ^  per  pound. 

HAM.    COMPL.    AKITII.  —  18 


274  PERCENTAGE 

5.  150  boxes  plate  glass  (each  25  plates  16  in.  by  24  in.), 
duty  $.08  per  square  foot. 

6.  800  yd.  Brussels  carpet  27  in.  wide,  valued  at  $  1.45 
per  yard.     Duty  40%  plus  $.44  per  square  yard. 

Explain  the  different  kinds  of  duty  in  this  problem. 

7.  500  boxes  cigars  (each  box  weighing  1  lb.  and  con- 
taining 100  cigars)  invoiced  at  $3.50.  Duty  25%  plus 
$4.50  per  pound. 

8.  The  specific  duty  on  macaroni  is  1|  $  per  pound.  If 
the  duty  is  $57.90,  find  the  number  of  pounds  imported. 

9.  A  department  store  in  Buffalo  imported  from  London 
3i  tons  (1.  T.)  of  woolen  blankets  invoiced  at  40  cents  per 
pound,  subject  to  a  specific  duty  of  22  cents  per  pound  and 
an  ad  valorem  duty  of  30%.     How  much  duty  was  paid? 

10.  A  merchant  imported  from  Sheffield,  England,  12  gross 
of  table  knives  costing  10s.  per  dozen  in  Sheffield.  If  the 
duty  was  $1.44  per  dozen  and  15%  ad  valorem,  and  trans- 
portation $9.60,  find  the  cost  per  dozen  delivered. 

11.  A  certain  painting  in  Rome  is  purchased  for  50000 
lire  ($  .193).  Find  the  cost  when  delivered  in  New  York,  if 
the  duty  is  20%  and  freight  and  insurance  $49.75. 

12.  Find  the  entire  cost  of  importing  3000  lb.  of  worsted 
yarn,  invoiced  at  £360,  if  the  freight  charges  are  $11.75; 
duty  27|^  per  pound  ;  and  40%  ad  valorem. 

13.  Brown  &  Co.  import  1200  sacks  of  cocoa,  each  contain- 
ing 90  lb.  If  the  duty  is  2±?  per  pound  and  tare  1  %,  find 
the  duty  on  the  goods  when  imported. 

14.  An  importer  paid  $480  duty  on  lace  on  which  he 
paid  a  duty  of  60  %.  If  the  lace  cost  50^  per  yard,  find  the 
number  of  yards  imported. 


INTEREST 

Interest  is  money  paid  for  the  use  of  money. 

The  principal  is  the  sum  loaned. 

The  amount  is  the  principal  plus  the  interest. 

The  rate  is  the  number  of  hundredths  of  the  principal  paid 
for  its  use  for  one  year. 

Time  is  always  a  factor  in  computing  interest. 

SIMPLE    INTEREST 

Simple  interest  is  interest  allowed  on  the  principal  only. 

Interest  is  generally  computed  on  the  basis  of  a  year  of 
12  months  of  30  days  each,  or  360  days.  This  is  called 
simple  or  common  interest. 

1.  How  much  is  the  interest  on  $200  at  6%  for  1  year? 
for  1  month  ?  for  15  days  ? 

2.  How  much  is  the  interest  on  $100  at  6%  for  1  year? 
for  1  month  ?  for  15  days  ? 

How  much  is  the  interest  at  6  %  on : 

3.  $100  for  11  years?  10.   $200  for  120  days? 

4.  $200  for  21  years?  11.  $60  for  1  year  1  month  ? 

5.  $200  for  6  months?  12.  $600  for  240  days? 

6.  $300  for  9  months  ?  13.  $300  for  30  days?  1  day  ? 

7.  $200  for  60  days?  14.  $500  for  11  mo.  12  da.? 

8.  $600  for  90  days9  15.  $700  for  6  mo.  15  da.  ? 
'   9.  $500  for  4  months ?  16.  $ 800  for  3  mo.  5  da.? 

•27."» 


276  INTEREST 

Written  Work 

1.    Find  the  interest  on  $600  for  2  yr.  9  mo.  at  6%. 

dh  />aa  i  Comparative  Study 

$600    =  principal  ,    m  , 

1.  The  principal  corresponds  to  what 

term  in  Percentage  ? 


$36.00    =illt.  for  1  yr.  o.  The   rate    corresponds    to   what 

2f       =time  in  years  term  in  Percentage  f 

$  27  =int.  for  9  mo.  <*.  The  interest  corresponds  to  what 

72        =int.  for  2  yr.  term  in  Percentaffe? 

1,  nn : — : — ;; tt-1 t. 4.  What  term  is  found  in  interest 

$99        =int.  tor  2  yr.  9  mo.  ,,    ,  .        ,e       ,  .     n        ,      9 

J  that  is  not  tound  in  Percentage  ? 

The  interest  equals  the  product  of  the  principal,  the  rate,  and 
the  time  expressed  in  years. 

Find  the  interest  on  : 

2.  $250  for  21  yr.  at  6%.  7.    $320  for  5  yr.  at  5J%. 

3.  $708  for  4  yr.  at  7%.  8.   $600  for  3^  yr.  at  6%. 

4.  $650  for  If  yr.  at  4%.  9.   $200  for  11  mo.  at  6%. 

5.  $800  for  10  mo.  at  6  %.  10.   $570  for  If  yr.  at  4%. 

6.  $260  for  If  yr.  at  4*  %.  11.    $290  for  3  yr.  at  6|%. 

Method  by  Aliquot  Parts  for  Years,  Months,  and  Days 

Written  Work 

1.    Find  the  amount  of  $  960  for  3  yr.  7  mo.  18  da.  at  5  % 

Principal  =  I960 
Rate         =     .05 
Int.  for  1  yr.  =  $  48.00 
Int.  for  3  yr.  =  3  x  $48,  or     $144.00 

Int.  for  6  mo.  =  *  of  $ 48,  or         24.00 

Int.  for  1  mo.  =  j\  of  $48,  or         4.00 

Int.  for  15  da.  =  \  of  $4.00,  or       2.00 

Int.  for 3  da.  =  T\  of  $4.00,  or        .40 

Int.  for  3  yr.  7  mo.  18  da.  =  $174.40 

Principal  =  960.00 

Amount  =  $1134.40. 


SIMPLE   INTEREST  277 

Find  the  amount  of  : 

2.  $1400  for  3  yr.  3  mo.  12  da.  at  6%. 

3.  $975  for  5  yr.  8  mo.  24  da.  at  4*  %. 

4.  $360  for  4  yr.  5  mo.  10  da.  at  5.]  %. 

5.  $480  for  2  yr.  9  mo.  15  da.  at  7%. 

6.  $2700  for  6  yr.  6  mo.  20  da.  at  o%. 

7.  $1040  for  4  yr.  9  mo.  18  da.  at  8  %  . 

8.  $176.45  for  3  yr.  7  mo.  25  da.  at  C  %. 

9.  $1840  for  5  yr.  4  mo.  27  da.  at  4|%. 

10.  81875  for  7  yr.  2  mo.  6  da.  at  8%. 

11.  8200  for  2  yr.  1  mo.  15  da.  at  6%. 

12.  $1200  for  1  yr.  8  mo.  10  da.  at  7%. 

13.  $97.30  for  3  yr.  3  mo.  3  da.  at  8%. 

14.  83500  for  2  yr.  7  mo.  24  da.  at  ('.%. 

Find  the  interest  on  : 

15.  81575  at  5%  from  Jan.  3,  1907  to  Sept.  5,  1909. 

16.  81790.80  at  4*  %  from  Sept.  8, 1906  to  Dec.  10,  1910. 

17.  $2005  at  3.]  %  from  June  12,  1906  to  Oct.  8,  1909. 

18.  $4000  at  4|  %  for  5  yr.  8  mo.  21  da. 

19.  $4670  at  5|  %  from  Oct.  10,  1906  to  June  5,  1907. 

20.  $2890  at  61  %  from  April  3,  1905  to  Oct.  1,  1908. 

21.  $290.75  at  6%  from  May  8,  1905  to  Sept.  19,  1908. 

22.  89S0.60  at  5'  %  from  Aug.  7,  1906  to  June  7,  1912. 

23.  $759.40  at  1%  from  May  9,  1907  to  June  10,  1909. 

24.  $800.50  at  4T\,  %  for  1  yr.  7  mo.  20  da. 

25.  8200.80  at  b\%  from  May  3,  1906  to  Sept.  5,  1911. 


278  INTEREST 

The  Sixty  Day  Six  Per  Cent  Method 

Since  the  interest  on  $100  at  6%  for  1  yr.  is  $6,  the  in- 
terest for  60  da.  Q  of  a  year)  =  jt  of  $6,  or  $1. 

How  much  is  the  interest  at  6  %  for  60  days  on  : 

1.  1200  3.   $300  5.    $150  7.    $125 

2.  $  50  4.    $     6  6.    $250  8.    $120 

Does  the  interest  in  each  problem  equal  j^  of  the  princi- 
pal? 

Written  Work 

1.  Find  the  interest  at  6%  on  $650  for  90  days. 

Interest  for  60  days  (2  mo.)  =  $6.50 
Interest  for  30  days  (1  mo.)  =  $3.25 
Interest  for  90  days  (3  mo.)  =  $9.75 

The  interest  of  any  principal  for  60  da.  (2  mo.)  at  6  %  is 
found  by  moving  the  decimal  point  in  the  principal  two  places 
to  the  left. 

Find  the  interest  at  6  %  on  : 

2.  $275  for  2  mo.  5.   $198  for  3  mo. 

3.  $  95  for  3  mo.  6.   $475  for  3  mo. 

4.  $172  for  3  mo.  7.   $280  for  3  mo. 

8.  Find  the  interest  at  6%  on  $345  for  8  mo. 

The  interest  for  2  mo.  =  $3.45,  or  T^5  of  the  principal 
The  interest  for  8  mo.  =  4  x  $3.45  =  $13.80 

Find  the  interest  at  6%  on: 

9.  $125  for  120  da.  13.    $805  for  75  da. 

10.  $190  for  4  mo.  14.    $425  for  2 1  mo. 

11.  $325.50  for  8  mo.  15.    $500  for  30  da. 

12.  $  62.50  for  240  da.  16.    $280  for  45  da. 


SIMPLE    INTEREST  279 

17.  $  600  for  6  mo. 

18.  $350  for  9  mo.  (8  mo.  +  1  mo). 

19.  $450  for  19  mo.  (18  mo.  +  1  mo.). 
Find  the  interest  at  6  <f0  on  : 

20.  $550  for  22  mo.  30.  8845.50  for  1  yr.  6  mo. 

21.  $640  for  18  mo.  31.  $850  for  1  yr.  2  mo. 

22.  8435  for  180  da.  32.  $392  for  1  yr.  4  mo. 

23.  $552  for  21  mo.  33.  $362  for  1  yr.  2  mo. 

24.  $632  for  120  da.  34.  $563.25  for  1  yr. 

25.  $562  for  16  mo.  35.  $147.50  for  1  yr. 

26.  $335  for  8  mo.  36.  $150  for  90  da. 

27.  $222  for  9  mo.  37.  $650  for  120 da. 

28.  $375  for  1  yr.  4  mo.         38.  $160  for  100  da. 

29.  $387.50  for  1  yr.  6  mo.      39.  $60.20  for  10  mo. 

40.    Find  the  interest  on  $562.50  for  1  yr.  10  mo.  15  da. 

at  6%. 

The  interest  for    2  ino.       =  $   5.625,  or  ^  of  the  principal 
The  interest  for  20  mo.       =    56.25,  or  10  x  5.625 
The  interest  for  15  da.        =       1-106,  or  \  of  15.625 
Int.  for  1  yr.  10  mo.  15  da.  =  *i>:J.2>>l 

Find  the  interest  at  6  $>  on  : 

41.  $  500  for  6  mo.  15  da.  49.    $175.50  for  105  da. 

42.  $250  for  8  mo.  20  da.  50.  $  150  for  9  mo.  12  da. 

43.  $360  for  5  mo.  10  da.  51.  $387.50  for  6  mo.  25  da. 

44.  $475  for  90  da.  52.  $125.50  for  10  mo.  21  da. 

45.  $900  for  6  mo.  25  da.  53.  $345.50  for  6  mo.  15  da. 

46.  $125  for  4  mo.  19  da.  54.  $  755  for  1  yr.  9  mo.  6  da. 

47.  $  325  for  6  mo.  23  da.  55.  $  544  for  5  yr.  3  mo.  5  da. 

48.  $25.50  for  3  mo.  29  da.  56.  8  80. SO  for  2  yr.  15  da. 


280  INTEREST 

57.  $5175  for  4  yr.  10  mo.  (60  mo.  — 2  mo.). 

58.  $640  for  3  yr.  2  mo.  (40  mo.  — 2  mo.). 

59.  $  1240.60  for  2  yr.  9  mo.  15  da. 

From  the  interest  on  any  principal  at  6  %,  the  interest  at 
other  rates  may  be  found  by  adding  or  subtracting  aliquot 
parts  of  the  interest  at  6  %  ',  thus, 

4  %  =  6  %  -  i  of  6  %         7-1  %  =  6  %  +  I  of  6  % 
41  %  =  6  %  -  J  of  6  %  8  %  =  6  %  +  £  of  6  % 

5  %  =  6  %  -  1  of  6  %  9  %  =  6  %  +  1  of  6  % 
7  cj0  =  6  %  +  \  of  6  %         10  %  =  i  of  6  %  x  10 

60.  Find  the  interest  at  5  %  on  $  360  from  May  1,  1905 
to  March  16,  1907. 

Time,  1  yr.  10  mo.  and  15  da.  =  22|  mo. 

Principal  =  $380.00 

Interest  of  $  360  for    20  mo.  at  6  %  =  $  36.00 

Interest  of  $360  for      2  mo.  at  6  %  =  3.60 

Interest  of  $  360  for      j  mo.  at  6  %  =  .90 

Interest  of  $360  for  22$  mo.  at  6  %  =  $40.50 

Less  interest  of  $  360  for  22}  mo.  at  1  %  =  6.75 

Interest  of  $360  for  22 h  mo.  at  5%  =  $33.75 

Find  the  interest  on  : 

61.  $216  from  July  25,  1891  to  Sept.  10,  1893,  at  6  %. 

62.  $348  from  Jan.  16,  1893  to  Feb.  4,  1896,  at  7  %. 

63.  $  650.40  from  April  19, 1903  to  March  4, 1906,  at  4  %. 

64.  $1200  from  Nov.  2,  1900  to  Oct.  19,  1903,  at  4|  % 

65.  $1800  from  Aug.  25,  1902  to  June  1,  1906,  at  4|  %. 

66.  $476.25  from  Aug.  19,  1902  to  June  1,  1906,  at  8  %. 

67.  $1600  from  Sept.  25,  1902  to  May  18,  1906,  at  4|  %. 

68.  $164.88  from  July  3,  1903  to  Dec.  31,  1905,  at  5  %. 


SIMPLE   INTEREST  281 

The  One  Dollar  Six  Per  Cent  Method 

The  interest  on  $1  for  30  da.  (1  mo.)  =  $.005. 
The  interest  on  $  1  for  1  da.  (^  of  $.005)  =  $  .0001. 

•  Change  the  time  to  months  and  days.  Since  the  interest  on 
$1  for  1  mo.  is  |  of  a  cent  and  for  1  da.  ^  of  a  mill,  the 
interest  on  one  dollar  ivill  be  ^  as  many  cents  as  there  are 
months  and  ^  as  many  mills  as  there  are  days.  Midtiply  the 
result  by  a  number  equal  to  the  number  of  dollars  in  the 
principal. 

Written  Work 

1.  What  is  the  interest  on  $240.60  for  2  jr.  3  mo.  13 

da.  at  6%? 

2  yr.  3  mo.  =  27  mo. 
Interest  on  $1  at  6  %  for  27  mo.  =  $.135 
Interest  on  $  1  at  6  %  for  13  da.    =  $.002$ 

Interest  on  $1  at  6%  for  2  yr.  3  mo.  13  da.  =  $.137$ 
Interest  on  $240.60  =  240.60  x  $.137 f,  or  $33.00 

Find  the  interest  at  6%  on  : 

2.  $  7450  for  93  da.  14.  $  8790  for  5  mo. 

3.  $  8400  for  65  da.  15.  $  8250  for  6  mo. 

4.  $  9800  for  40  da.  16.  $  150  for  3  mo.  6  da. 

5.  $  8440  for  72  da.  17.  $  180  for  5  mo.  9  da. 

6.  8  5500  for  5  da.  18.  #195  for  6  mo.  10  da. 

7.  $  0750  for  8  da.  19.  $  250  for  8  mo.  12  da. 

8.  1 4765  for  25  da.  20.  $  340  for  2  yr.  4  mo. 

9.  8  6245  for  110  da.  21.  $275  for  3  yr.  8  mo. 

10.  $8425  for  52  da.  22.  $450  for  1  yr.  5  mo. 

11.  $  5150  for  3  mo.  23.  $  675  for  3  yr.  7  mo. 

12.  *  8465  for  4  mo.  24.  $64.60  for  2  yr.  9  rao. 

13.  8  9640  for  7  1110.  25.  $78.40  for  4  yr.  3  mo. 


282  INTEREST 

Find  the  interest : 

26.  At  5%  on  $  237.50  from  Jan.  3, 1906  to  Sept.  11, 1908. 

27.  At  7%  on  $309.75  from  May  5,  1905  to  Jan.  12, 1907. 

28.  At  7|  %  on  $  7500  from  June  12, 1907  to  Nov.  1,  1909. 

29.  At  61%  on  $  6225  from  Oct.  11, 1907  to  Mch.  1, 1910. 

30.  At  A\%  on  $750  from  Feb.  12,  1907  to  Aug.  9, 1911. 

31.  At  8%  on  $2900  from  July  1,  1906  to  May  10,  1910. 

32.  At  4%  on  $3675  from  June  4,  1907  to  Apr.  1,  1910. 

33.  At  3%  on  $  290.80  from  Nov.  12, 1907  to  Apr.  10, 1912. 

34.  At  5%  on  $875  from  June  11,  1907  to  Mch.  11,  1912. 

35.  At  5|%  on  $8000  from  Apr.  1,  1907  to  May  9,  1912. 

Solve   the  following  problems  by  both  the  six  per  cent 
methods  and  compare  results  as  to  time  and  accuracy. 

Find  the  interest  from  the  following  conditions: 


Prin. 

Time 

Rate 

Prin. 

Time 

Rate 

36.    $350 

105  da. 

1% 

39.    $129 

23  mo. 

9% 

37.  $685 

4  mo. 

8% 

40.  $750 

13  mo. 

n% 

38.  $850 

87  da, 

6% 

41.  $492 

97  da. 

H% 

42.   Fin 

d  the  amount  of 

$1275.80  for  1  yr 

.  7  mo. 

24  da. 

at  1%. 

43.  Find  the  interest  of  $4780  from  April  1,  1907  to 
Sept.  18,  1909,  at  6|%. 

44.  On  the  16th  of  September,  1907,  I  borrowed  $3600  at 
8  %.     How  much  will  settle  the  loan  April  1,  1909  ? 

45.  July  28,  1907,  a  broker  borrows  $3200  at  5%  in- 
terest and  on  the  same  day  loans  it  at  7|  %  interest.  If  full 
settlement  is  made  April  1,  1909,  how  much  will  the  broker 
make  by  reloaning  the  money  ? 


PROBLEMS   IN   SIMPLE    [NTEREST  283 

PROBLEMS  IN  SIMPLE  INTEREST 
Finding  the  principal. 

Written  Work 

1.  What  principal  invested  at  4  %  per  annum  will  yield  an 

annual  income  of  $200  ? 

Since  the  interest  on  $  1  for  1  year  at  4%  is  $.04,  as  many  dollars  must 
be  invested  to  yield  8200  per  year  as  $.04  is  contained  times  in  $200. 
$200  h-  $.04  =  5000.     Hence,  $5000  must  be  invested. 

TJie  principal  equals  the  given  interest  divided  by  the  interest 
on  $lfor  the  given  time  at  the  given  rate. 

2.  What  principal  at  4£%  will  gain  $213.75  interest  in 
4  yr.  9  mo.? 

3.  What  principal  at  5%  will  gain  $120.70  interest  in 
3  yr.  6  mo.  18  da.? 

4.  What  principal  at  8%  will  gain  an  interest  of  $163.20 
from  Sept.  30,  1903  to  June  12,  1905  ? 

5.  A  man  gave  his  note  April  1,  1901,  at  6%.  When  he 
settled  the  note  Aug.  13,  1903,  he  paid  $195.25  interest. 
What  was  the  principal,  or  face  of  the  note  ? 

Finding  the  rate. 

Written  Work 

1.  At  what  rate  must  $500  be  invested  to  yield  $75 
interest  in  2  yr.  6  mo.  ? 

Since  the  interest  on  $500  for  2\  yr.  at  1%  is  $12.50,  it  will  require 
a  rate  of  as  many  per  cent  to  yield  $75,  as  $12.50  is  contained  times  in 
$75,  or  6%. 

The  rate  equals  the  given  interest  divided  by  the  interest  for 
the  given  time  at  1  %  • 

2.  The  interest  on  $1125  for  3  yr.  4  mo.  24  da.  is  $229.50. 
What  is  the  rate  per  cent  ? 


284  INTEREST 

3.  The  interest  on  $1800  for  4  yr.  8  mo.  16  da.  is  1424. 
What  is  the  rate  ? 

4.  At  what  rate  will  $2460  give  $682.65  interest  in  5  yr. 
6  mo.  18  da.? 

5.  A  note  for  $880  was  given  July  5,  1900,  and  settled 
May  2,  1904,  for  $1081.96.     What  rate  per  cent  was  charged? 

Finding  the  time. 

Written  Work 

1.  In  what  time  will  $450  at  0%  yield  $90  interest? 

Since  the  interest  on  -1450  for  1  yr.  at  6%  is  $27,  the  required  time  is 
as  many  years  as  $ 27  is  contained  times  in  $90,  or  3$  yr. 

The  time  in  years  equals  the  given  interest  divided  by  the 
interest  at  the  given  rate  for  1  year. 

2.  In  what  time  will  $275  gain  $55  interest  at  6  %  ? 

3.  In  what  time  will  any  principal  double  itself  (that  is, 
gain  100  %  of  itself)  at  5  %  ?  at  6  %  ?  at  8  %  ? 

4.  In  what  time  will  any  principal  treble  itself  (that  is, 
gain  200%  of  itself)  at  5  %?  at  6  %  ?  In  what  time  will  it 
quadruple  itself  at  8  %  ?   at  10  %  ? 

5.  A  note  of  $500  at  5%  interest  was  paid  May  1,  1905, 
the  interest  amounting  to  $63.75.  When  was  the  note 
given? 

REVIEW   PROBLEMS 

1.  Find  the  interest  on  $80  for  6  yr.  6  mo.  18  da.  at  6  %. 

2.  In  what  time  will  $180  at  5  %  yield  $22.50  interest? 

3.  In  what  time  will  $600  amount  to  $715.50,  at  5|% 
interest  ? 


REVIEW   PROBLEMS  285 

4.  At  what  rate  will  $1650  gain  #326.70,  in  4  yr.  4  mo. 
24  da.? 

5.  What  sum  of  money  loaned  at  0%  will  give  a  semi- 
annual income  of  $13.02  ? 

6.  Interest  $31.80;  time  3  yr.  6  mo.    12  da.;   rate  5%. 
Find  the  principal. 

7.  The  interest  of  ^  of  a  principal  for  3  yr.  6  mo.  at  6% 
is  $19.25.     Find  the  principal. 

8.  If  $186  pays  a  debt  of  $150  which  has  been  due  for 
4  years,  what  is  the  rate  of  interest  ? 

9.  I  borrowed  $450  at  5%  and  kept  it  until  it  amounted 
to  $525.     When  did  I  settle  the  note  ? 

10.  Dec.  1, 1901, 1  loaned  $300  at  5*  %.  Find  the  amount 
due  March  16,  1905. 

11.  Find  interest  at  6%  on  $350  from  June  1,  1898  to 
Aug.  13,  1902. 

12.  If  $300  was  borrowed  April  1,  1902,  at  5%,  when 
should  the  principal  and  interest  be  paid  that  their  sum  may 
be  $357? 

13.  The  amount  of  a  certain  principal  at  6  %  for  a  given 
time  is  $780,  and  at  10%  for  the  same  time  it  is  $900. 
Find  the  principal. 

14.  If  $148  is  loaned  April  1,  1902,  at  5%,  when  will  it 
amount  to  $179.45  ? 

15.  What  principal  for  3  mo.  at  8  r/c  will  yield  the  same 
interest  as  $5100  for  5  yr.  8  mo.  at  6  %  ? 

16.  A  farmer  bought  75  acres  of  land  at  $  50  an  acre, 
paying  ^  cash,  and  giving  his  note  for  the  balance,  due  in 
3  yr.  6  mo.,  with  interest  at  6%.  What  was  the  amount  of 
the  note  at  maturity  ? 


286 


INTEREST 


ANNUAL    INTEREST,    OR     SIMPLE     INTEREST    ON    UNPAID 

INTEREST 

In  some  states  when  a  note  reads  with  interest  "  payable 
annually,"  simple  interest  may  be  collected  upon  the  princi- 
pal and  upon  each  year's  interest  from  the  time  it  was  due 
until  paid. 

In  most  states  annual  interest  is  not  collectable  by  law. 

Interest  payable  annually  is  simple  interest;  but  interest  collected 
on  the  principal  and  on  the  overdue  payments  of  simple  interest  is 
annual  interest. 

Written   Work 

1.  James  Brown  borrows  $1200  at  6%  interest,  "payable 
annually."  In  case  no  interest  is  paid  for  3  years,  6  months, 
and  15  days,  how  much  money  is  necessary  to  pay  the  debt  ? 


Simple  interest  on  $  1200,  at  6%,  for  3  yr.  6  mo.  15  da. 
The  interest  for  each  year  is  $72. 

The  1st  annual  int.,  $72,  remains  unpaid  for  2  yr.  6  mo.  15  da. 
The  2d  annual  int.,  $72,  remains  unpaid  for  1  yr.  6  mo.  15  da. 
The  3d  annual  int.,  $72,  remains  unpaid  for  6  mo.  15  da. 

Interest  on  $72  at  6%  for         .         .         .       4  yr.  7  mo.  15  da. 

The  annual  interest  on  $1200  for  3  yr.  6  mo.  15  da. 
The  principal         ...         ..... 

The  amount  of  $  1200  at  annual  interest  for  3  yr.  6  mo.  15  da. 


255 


19 


274 
1200 


1474 


98 
98 
00 

98 


Annual  interest  is  the  simple  interest  on  the  principal  for 
the  given  time  plus  the  simple  interest  on  each  year's  interest 
for  the  time  it  remains  unpaid. 

2.  Find  the  total  interest  due  on  a  note  of  $  675  for  2  years, 
8  months,  and  20  days  at  6%,  with  interest  payable  annu- 
ally, if  no  interest  has  been  paid. 

3.  Find  the  amount  of  $6400  for  4  years,  5  months,  and 
15  days,  with  interest  payable  annually  at  6  (f0. 


EXACT    INTEREST  lis; 

4.  An  attorney  collects  a  note  of  $3750  with  annual  in- 
terest on  it  at  6%  for  4  yr.  9  mo.  18  da.  Kind  the  amount 
collected  and  his  commission  on  it  at  10%. 

EXACT  INTEREST 
Exact  interest  is  simple  interest  on  the  principal  reckoned 
on  the  basis  of  365  days  to  a  common  year  and  366  days  to  a 
leap  year. 

It  is  used  in  computing  interest  on  all  obligations  by  the  United 
States  government ■;  on  all  foreign  securities;  and  to  some  extent  by  city 
controllers  and  bankers. 

Since  common  interest  is  computed  on  the  basis  of  12  months  of  30 
days  each,  or  360  'lays  ;  and  exact  interest  is  reckoned  on  the  basis  of  365 
days  to  a  common  year,  or  366  to  a  leap  year,  1  day's  exact  iuterest 
is  jl-s  of  a  year's  common  interest. 

It  is  evident  that  the  common  and  exact  interest  for  1  year  are  the 
same.  Thus,  fff  of  one  year's  common  interest  equals  one  year's  exact 
interest.     They  differ  only  for  parts  of  a  year. 

Written  Work 

1.    Find  the  exact  interest  on  $2400  for  95  days  at  6%. 

Exact  interest  for  1  year  =  6%  of  $2400,  or  $144 
Exact  interest  for  1  day  =  -353  of  $144,  or  $.394.") 
Exact  interest  for  95  days  =  95  x  $.3945,  or  $37.48 

Exact  interest  is  found  by  dividing  the  common  interest  at  the 
given  rate  for  one  year  by  365  and  multiplying  the  quotient  by 
the  exact  number  of  days. 

Find  the  exact  interest  of: 

2.  6800  for  78  days  at  6  % .       6.  $500  for  90  days  at  9  %. 

3.  $2000  for  92  clays  at  7%.      7.  $1020  for  74  days  at  10%. 

4.  62400  for  115  days  at  8%.    8.  $6500  for  280  days  at  6%. 

5.  61775  for  100  days  at  8|%.   9.  $10000  for  61  days  at  7%. 
10.    Find  the  exact  interest  on  $1020  from  Oct.  19,  1905 

to  April  1,  1907,  at  6%. 


288 


INTEREST 


Notk.  —  Why  do  we  find  exact  interest  for  a  fraction  of  a  year  only  V 
The  exact  number  of  days  from  Oct.  19,  1905  to  April  1,  1907,  is  found 
as  follows :  Oct.,  12  da. ;  Nov.,  30  da.  ;  Dec,  31  da. ;  Jan.,  31  da. ;  Feb. 
28  da. ;  March,  31  da. ;  April,  1  da.     Total,  164  days. 

11.  Find  the  exact  interest  on  $1795.80  from  July  7, 1901 
to  Sept.  1,  1907  at  7%. 

12.  The  United  States  government  paid  exact  interest  at 
4  (f0  on  a  warrant  of  $ 650000,  83  days  past  due.  Compute 
the  amount  paid. 

COMPOUND    INTEREST 

Mr.  Reed  Colburn  loans  Robert  Patterson  $200  for  2 
years  at  6  % . 

Suppose  Mr.  Patterson  says  to  Mr.  Colburn,  at  the  end  of  the  first 
year  :  "  I  cannot  pay  you  the  $  12  interest  due,  but  will  pay  you  interest 
at  6  %  on  the  $12  for  a  year."  How  much  interest  should  Mr.  Patterson 
pay  Mr.  Colburn  at  the  end  of  the  2  years?  How  does  the  12-1.72  inter- 
est differ  from  simple  interest? 

Compound  interest  is  interest  on  both  the  principal  and 
the  unpaid  interest  added  to  the  principal  when  due. 

Interest  may  be  added  to  the  principal  annually,  semiannually,  or 
quarterly,  according  to  agreement. 


Written  Work 
1.    Find  the  compound 


months  at  0%. 


Principal 

Interest  for  1st  yr.  atG  % 
Principal  for  2d  year 
Interest  for  2d  yr.  at  6  % 
Principal  for  3d  yr. 
Interest  for  6  mo.  at  6  % 
Amount  for  2  yr.  6  mo.  at  6  % 
Original  principal 
Compound  interest  for  2  yi 


iterest  on   $200 

for 

2   years    6 

$200.00 

. 

12.00 

.                  , 

212.U0 

.                  , 

12.72 

.                  . 

224.72 

.                 . 

6.74 

6%     • 

231.46 

. 

►                           o 

200.00 

.  G  mo.  at  ( 

i%  •     ■ 

31.46 

SAVINGS    ACCOUNTS  289 

Note. —  1.    Unless  otherwise  stated  in  the  agreement,  interest  is  com- 
pounded annually. 
2.    When    interest    is   compounded  semiannually,   consider   the   rate 

as  A   the  annual  rate,  or  if  quarterly,  £,  etc. 

2.  Find  the  compound  interest  on  $1000  for  2  years  at 
5%,  with  interest  compounded  semiannually. 

3.  Find  the  compound  interest  at  6%  on  $800  for  1  yr. 
5  mo.,  interest  payable  quarterly. 

4.  Find  the  compound  interest  on  $600  for  9  mo.  at  6%, 
interest  payable  quarterly. 

SAVINGS  ACCOUNTS 

Compound  interest  is  no  longer  allowed  on  notes.  Its 
only  practical  application  for  elementary  schools  is  found  in 
computing  interest  on  savings  accounts. 

Many  banks  to-day  have  a  savings  department.  The  amounts  thus 
deposited  are  not  subject  to  check,  but  draw  from  2%  to  4%  interest 
which  is  usually  compounded  semiannually. 

The  interest  periods  are  generally  January  1  and  July  1 
of  each  year,  although  sometimes  the  interest  is  compounded 
quarterly.     Thirty  days  are  reckoned  to  a  month. 

Interest  on  savings  accounts  is  sometimes  calculated  from  the  1st  and 
15th  of  each  month  succeeding  the  serend  dejiosits.  Thus,  $  10  deposited  on 
the  1st  of  any  month  would  draw  interest  from  date;  but  $10  deposited 
on  the  2c?  of  any  month  would  draw  interest  from  the  loth:  or  money 
deposited  on  the  16th  wrould  draw  interest  from  the  1st  of  the  next 
month.  There  is  no  fixed  rule,  however,  as  each  bank  determines  for  itself 
when  the  interest  date  begins.  No  interest  is  allowed  on  a  fractional 
part  of  a  dollar,  and  parts  of  a  cent  are  omitted  on  all  interest  credits. 

Most  banks  require  notice  from  a  depositor  before  a 
savings  account  may  be  withdrawn.  Amounts  withdrawn 
before  the  end  of  an  interest  period  draw  no  interest  for 
that  period. 

HAM.    COMPL.     A  KITH. —  19 


290 .  INTEREST 

Written  Work 

1.  On  July  1,  1905,  Raymond  Wilkinson  makes  a  sav- 
ings deposit  of  $400  at  4%  interest,  payable  semiannually. 
If  the  interest  at  each  period  is  added  to  the  deposit,  what 
is  the  total  amount  in  bank  January  1,  1907  ? 

Deposit  July  1,  1905 $400.00 

Interest  on  $400  at  4  %  July  1,  1905  to  Jan.  1,  1906       .        ..  8.00 

Amount  in  bank  Jan.  1,  1906 408.00 

Interest  at  4  %  on  $408  from  Jan.  1,  1906  to  July  1,  1906       .  8.16 

Amount  in  bank  July  1,  1906         ......  416.16 

Int.  at  4  %  on  $416  (why?)  from  July  1,  1906  to  Jan.  1,  1907  8.32 

Amount  in  bank  Jan.  1,  1907 424.48 

2.  Find  the  difference  between  the  simple  interest  on  a 
note  of  8200  dated  July  1,  1906,  due  in  two  years  at  4|  %, 
and  the  interest  on  $ 200  deposited  in  a  savings  bank  at  4  %, 
compounded  semiannually,  for  the  same  period. 

3.  A  savings  account  of  $150  deposited  April  1,  1906, 
at  3%  interest,  payable  January  1  and  July  1,  is  with- 
drawn April  12,  1908.     Find  the  amount  withdrawn. 

4.  A  savings  bank  pays  4%  interest,  calculated  from  the 
1st  and  the  loth  of  each  month  succeeding  the  several  de- 
posits. The  deposits  are  Sept.  1,  $20;  Oct.  10,  $15;  Nov. 
15,  $20;  Dec.  10,  $25.  Find  the  amount  in  bank  the 
following  January  1,  if  the  interest  periods  are  January  1 
and  July  1. 

5.  The  Lincoln  School  had  on  deposit  in  the  Holmes  Sav- 
ings Bank  Jan.  1,  1907,  $495.80.  The  deposits  were  as  fol- 
lows: Feb.  1,  $76.90;  March  1,  $105.05;  April  1,  $114.29; 
May  1,  $129.70;  June  1,  $98.75.  Find  the  amount  in  the 
bank  Jan.  1,  1908,  at  4  %  interest,  compounded  the  first  of 
January  and  July. 


INVESTMENTS 


291 


Find  the  amount  in  bank  from  the  following  deposits 


Deposit 

Date 

Rate 

Int.  Payable 

Amount  in  Bank 

6. 

$200 

Jan.  1,  1905 

3% 

Jan.  1  and  July  1 

July  1,  1906 

7. 

$150 

Mar.  16,  1906 

4% 

Jau.  1 

Jan.  1,  1908 

8. 

$875 

May  29,  1906 

21  % 

Jan.  1 

Jan.  1,  1908 

9. 

$1200 

Aug.  10,  1906 

2% 

Jan.  1,  Apr.  1, 
July  1,  Oct.  1 

Jan.  1, 1908 

INVESTMENTS 

Compound  interest  tables  are  frequently  used  by  insurance 
companies,  building  and  loan  associations,  and  trust  com- 
panies, to  calculate  the  income,  from  investments  where  the 
interest  is  added  each  interest  period  to  the  amount  invested. 

The  following  table  shows  the  amount  of  $1  at  compound  interest  at 
the  given  rates  for  10  years. 


Compound  Interest  Table 


Yr. 

n% 

2% 

n% 

3% 

n% 

4% 

1 

1.0150  000 

1.0200  0000 

[.0250  in ii  10 

1.0300  0000 

1.0350  0000 

1.0400  0000 

8 

1.0302  250 

1.0404  0000 

1.0506  2500 

1.0609  0000 

1.0712  2500 

1.0816  0000 

3 

1.0456  784 

1.0612  0800 

1.0768  9062 

1.0927  2700 

1.1087  17S7 

1.1248  6400 

4 

1 .0618  636 

1.0824  3216 

1.1088  1289 

1.1255  0881 

1.1475  2300 

1.1698  5856 

5 

1.0772  840 

1.1040  8080 

1.1314  0821 

1.1592  7407 

t.1876  8631 

1.2166  5290 

6 

1. 0984  488 

1.1261  6242 

1.1596  9342 

1.1940  5230 

1.2292  5533 

1.2653  1902 

7 

1.1098  (50 

1.1486  8567 

1.1886  8575 

L.2298  7887 

1.2722  7926 

1.S159  8178 

8 

1.1264  926 

1.1716  5938 

1.2184  0290 

1.2667  7008 

1.3168  0904 

1.3685  6905 

9 

1.1488! 

1.1951)9257 

1.2488  6297 

1.3H47  7318 

1.3628  9735 

1.4288  1181 

10 

1.1605  408 

1.2189  9442 

1.2800  8454 

1.8489  1688 

1.4105  9876 

1.4802  (423 

The  compound  interest  on  any  amount  for  4  years  at  8%  payable 
semiannually  is  evidently  the  same  as  upon  the  same  amount  for  8  years 
at  4  %  payable  annually. 

The  amount  of  any  given  principal  for  any  given  number 
of  years  is  found  by  multiplying  the  principal  by  the  amount 
of  $1  at   the   given  rate  for  the  time  as  given  in  the  table. 


202  INTEREST 

Written  Work 

1.  Find  the  amount  of  $1200  invested  for  7  years  at  3^  %, 
interest  compounded  annually. 

2.  Find  the  compound  interest  at  4  %  on  $  10000  invested 
for  9  years. 

3.  The  amount  of  $12000,  invested  for  10  years  at  31  %, 
interest  compounded  annually,  is  divided  equally  among 
3  sons.     Find  each  one's  share. 

4.  Find  the  amount  of  $1200  for  2  years  and  6  months 
at  4  %,  compound  interest  payable  semiannually. 

PROMISSORY   NOTES 

Mr.  James  H.  Ames,  a  grocer,  Erie  St.,  Buffalo,  N.Y.,  has 
an  account  of  $52.00  against  Robert  Patterson  for  groceries, 
and  Mr.  Ames  asks  Mr.  Patterson  to  give  him  a  note  at  6  % 
interest  for  the  amount  of  the  bill. 

The  note  reads  as  follows  : 


$52.00  Buffalo,  JV.T.,  Mv-.  Bf,  1905. 

c/ux,  'nvcyyttJt^  after  date -_.c/---  promise  to  pay  to  the 

order  of jtawvea-  /if.  CL,wu&^ 

&C££y  - 1  w-  cirrrrrrrrrr?ccrr^'rrrrrr^rcc'rrrr^^  /  ars. 

Value  received,  with  interest  at  6%. 

f\ot>evt  ^utt&VQycyyv. 


1 


A  promissory  note  is  a  written  promise  to  pay  to  a  certain 
person  named  in  the  note,  or  his  order,  a  specified  sum  of 
money  at  a  specified  time. 


PROMISSORY    NOTES  293 

The  Essentials  of  a  Promissory  Note : 

1.  It  should  state  the  place  where  and  the  time  when  given. 

2.  It  should  promise  to  pay  to  a  certain  person  or  to  his  order. 

3.  It  should  promise  to  pay  a  certain  sum  of  money,  expressed  both  in 
figures  and  in  writing. 

4.  It  should  state  when  the  money  is  to  be  paid. 

5.  It  should  state  by  whom  the  money  is  to  be  paid. 

6.  It  should  state  for  value  received. 

(Xot  absolutely  necessary,  but  usually  written  in  a  note.) 

7.  It  should  state  with  interest  and  tlie  rate,  if  it  is  an  interest-bearing 
note. 

The  promissor  is  called  the  maker  of  the  note. 
The  person  who  is  to  receive  the  money  is  called  the  payee 
of  the  note. 

1.  Who  is  the  maker  of  the  note  on  page  292? 

2.  Who  is  the  payee  of  the  note  on  page  292? 

3.  Find  the  amount  to  be  paid  when  due. 

4.  The  face  of  the  note  is  the  sum  written  in  the  note.  What  is  the 
face  of  the  note  on  page  292? 

5.  This  note  reads  "pay  to  the  order  of  James  H.  Ames,"  and  mean- 
that  Mr.  Ames  has  the  right  to  sell  this  note  to  any  one  by  simply  writing 
his  name  across  the  back  of  the  note  and  delivering  it  to  the  purchaser. 
What  words  in  the  above  note' give  Mr.  Ames  the  right  to  sell  it? 

When  the  owner  of  a  promissory  note  writes  his  name 
across  the  back  of  it,  he  is  said  to  indorse  the  note. 

If  Mr.  Ames  indorses  the  note  and  then  sells  it  to  Mr.  B..  and  Mr.  B. 
indorses  it  and  sells  it  to  Mr.  C,  to  whom  does  the  note  belong? 

A  promissory  note,  therefore,  like  any  other  property 
may  be  bought  and  sold  ;  hence  it  is  called  negotiable  paper. 

When  a  note  is  made  payable  to  a  definite  person,  it  cannot  be  trans- 
ferred, and  is  therefore  nut  negotiable. 


294 


INTEREST 


jlavi'&&  CLnd&x^o-ru. 


Indorsement  in  Full 


Promissory  notes  may  be  indorsed  as  follows: 

Indorsement  in  Blank 

(1)  In  blank :  In  this  form  the 
indorser  simply  writes  his  name 
across  the  back  of  the  note,  thus 
making  the  note  payable  to  the 
holder. 

(2)  In  full :  In  this  form  the  in- 
dorser designates  that  the  note  is 
to  be  paid  to  the  order  of  a  definite 
person. 

(3)  In  limited  form :  In  this  form 
the  indorser  writes  ''without  re- 
course "  above  his  name.  This 
means  that  the  holder  cannot  com- 
pel him  to  pay  if  the  maker  fails 
to  do  so.  lAJ-iZkout  \,e&cm,'v&&. 


&aAf  to-  tk&  o'uLeA,  o 


Limited  Indorsement 


/ 


Every  indorser  in  blank,  or  in  full, 
makes  himself  liable  for  the  amount  of 
the  note  if  the  maker  and  the  previous 
indorsers /a;7  to  pay.     Banks  are  required 

to  notify  the  indorsers  in  a  manner  prescribed  by  law  in  case  the  note  is 
not  paid  when  due.  This  is  called  protesting  the  note.  If  the  note  is 
not  protested,  the  indorsers  are  released  from  the  liability  of  payment. 

Forms  of  promissory  notes. 

I.    As  to  time : 

1.  If  the  words  "on  demand"  are  substituted  for  the  words  "six 
months  "  in  the  note  of  Mr.  Ames,  page  2.c)2,  it  will  then  be  a  "  demand 
note  " ;  that  is,  the  maker  may  be  called  upon  to  pay  it  at  any  time  after 
date. 

2.  The  note  of  Mr.  Ames  is  a  "time  note"  because  it  is  not  to  be 
paid  until  a  certain  time  named  in  the  note. 

The  time  of  payment  in  a  note  must  be  definite.  A  promise  to  pay 
"  when  able  "  is  too  indefinite,  and  not  binding. 


PROMISSORY    NOTES  295 

II.  As  to  payees  : 

1.  When  a  note  is  payable  to  the  order  of  some  particular  person,  he 
alone  can  collect  it,  or  sell  the  note  by  indorsement. 

2.  When  a  note  is  payable  to  some  particular  person,  or  bearer,  the 
holder  can  collect  it,  or  sell  it  by  indorsement. 

III.  As  to  the  number  of  makers  : 

1.  An  individual  note  is  a  promise  made  by  one  person. 

2.  "  A  joint  and  several  note  "  is  a  promise  made  by  more  than  one 
person.  It  contains  the  words  "  we,  or  either  of  us,"  and  is  signed  by 
the  makers. 

Maturity  of  Promissory  Notes. 

A  note  is  said  to  mature  on  the  last  day  of  the  time  named  in  the  note. 
Some  states  allow  3  days,  called  "  days  of  grace,"  from  the  time  a  note 
matures  before  the  payee  can  proceed  to  collect  the  note.  In  this  case 
three  days  are  added  to  the  time  on  which  the  interest  is  computed. 
Days  of  grace  are  now  abolished  in  most  states.  The  note  on  page  2i)'J 
matures  May  21,  1906. 

If  a  note  falls  due  on  Saturday,  Sunday,  or  a  legal  holiday,  it  is  usu- 
ally payable  on  the  next  succeeding  business  day.  Some  states  require 
such  notes  to  be  paid  on  the  preceding  business  day. 

Interest  on  Promissory  Notes. 

If  either  a  time  or  a  demand  note  contains  the  words  "with  interest," 
the  note  bears  interest  from  date  at  the  legal  rate  in  that  state. 

If  the  words  "with  interest"  ai-e  omitted  from  a  time  note,  it  bears 
interest  from  the  date  of  maturity  until  paid. 

If  the  words  "  with  interest  "  are  omitted  from  a  demand  note,  it  bears 
interest  from  the  time  payment  is  demanded  until  paid. 

Written  Work 

1.  Is  the  promissory  note  given  by  Mr.  Patterson  (p.  292) 
a  demand  or  a  time  note?  an  individual  or  a  joint  and  sev- 
eral note  ?  payable  to  order  or  bearer  ? 

2.  Write  a  promissory  note,  in  which  you  are  the  maker, 
for  $125  due  in  6  months,  payable  to  the  order  of  Ellsworth 
Slater,  with  the  legal  rate  of  interest  in  your  state. 


296  INTERp;ST 

3.  Mr.  Slater  sells  this  note  to  Herman  Gross,  and  in- 
dorses it  in  full.      Write  the  indorsement  on  the  note. 

4.  Write  a  joint  and  several  note  for  8250,  dated  Sept. 
24,  1905,  due  on  demand,  with  interest  at  6%,  payable  to 
the  order  of  James  Harbison.  Your  teacher  and  yourself 
may  sign  this  note  as  makers. 

5.  May  the  two  names  to  the  above  note  be  written  by 
the  same  person  ?     Why  not  ? 

6.  In  case  James  Harbison  sells  this  note  to  James  Brown, 
but  says  to  Mr.  Brown,  "  I  shall  not  be  responsible  for  the 
collection  of  this  note,"  write  the  indorsement  and  explain 
why  you  use  that  form. 

7.  Find  the  amount  paid  to  the  holder  of  Mr.  Harbison's 
note  (Ex.  4),  if  settled  Jan.  4,  1907. 

Note.  —  Time  from  Sept.  24,  1905  to  Jan. 4, 1907, 1  yr.,  4  mo.,  1 1  da. 

8.  Name  the  different  kinds  of  negotiable  notes  : 

(1)  as  to  time  ;  (2)  as  to  payee  ;  (3)  as  to  number  of  makers. 

9.  Find  the  amount  to  be  paid  on  the  following  note,  if 
settled  March  1,  1907 : 

The  note  is  legally  due  June  1,  1906;  therefore  it  bears  interest  at  the 
legal  rate  from  that  date. 


$300.00  Chicago,  171.,  iHoA^k  /,  1906. 

&ki&&  wuyn&kb  after  date ■.__ .J __  promise  to  pay  to  the 

order  of  Qavi&a,  6vy&& 

Value  received. 


PROMISSORY    NOTES  297 

10.    Find  the  interest  to  be  paid  on  the  following  note,  if 
settled  Aug.  10,  1906,  with  interest  at  6  %  ' 


$/75.60  Boston,  Mass.,  fam,.  20,  I<?06. 

Hrv  d&wuwul  after  date— J—  promise  to  pay  to  the 

order  of  3~kex>cLav&  <Ao&l 

dne,  hxincUvbcl  &&v&itty-'flv-&  i^rrrrrrrrrrrccccc'rrrr:  Dollars. 

Value  received,  with  interest. 

Clxtkiov  71'lawn. 


11.  If  the  words  "  with  interest "  are  not  mentioned  in  a 
time  note,  from  what  date  does  the  note  bear  interest? 

12.  If  a  note  reads  "  with  interest,"  and  no  rate  is  men- 
tioned, what  rate  per  cent  is  to  be  taken? 

13.  If  the  words  "with  interest"  are  not  written  in  a 
demand  note,  does  it  ever  bear  interest? 

14.  If  days  of  grace  are  allowed  in  your  state,  how  do  you 
find  the  time  on  which  the  interest  is  to  be  reckoned? 

15.  How  do  you  compute  time  on  a  promissory  note? 

16.  Which  is  the  safer  form  : 

Pay  to  the  order  of  Henry  James,  or 

Pay  to  the  order  of  Henry  James  or  bearer?    Why? 

Note.  —  The  note  of  Mr.  Ames  (p.  292)  could  have  been  made  payable  to 
James  H.  Ames   or  bearer.     Why  is  the  form  as  written  in  the  note  better  ? 

It  is  safest  to  indorse  a  note  in  full,  for  the  reason  that  if  it  is  lost  in 
its  delivery  by  mail  or  messenger,  it  can  be  collected  only  by  the  party 
named  on  the  back  of  it. 


298 


INTEREST 


Write  negotiable  notes,  observing  the  essential  conditions 
as  given  on  p.  293,  and  adding  days  of  grace  if  allowed  in 
vour  state.  Find  the  amount  due  at  date  of  settlement.  On 
overdue,  non-interest  bearing  notes,  compute  interest  at  6%. 


Date 

Face 

Time 

Payee              Maker 

Int. 
Rate 

Settle- 
ment 

1. 

•2/  5  /05 

$  100   6  months 

George  Kimes  Yourself 

6% 

Maturity 

2. 

4/21/06 

250  On  demand 

A.  J.  Edwards  James  Clyde 

8% 

7/29/06 

3. 

6/10/05 

500      1  year 

John  Dunn 

John  Grant 

(     ) 

6/15/07 

4. 

8/16/04 

350   6  months 

N.  J.  Noel 

James  Palm 

(     ) 

12/15/05 

5. 

7/12/05 

125  On  demand 

James  Bryce 

Yourself 

7% 

1  /  2  /06 

6. 

5/15/05 

1200 

3  months 

M.  J.  Boyce 

B.  J.  Morrow 

H% 

Maturity 

7. 

10/10/05 

300 

6  months 

Ralph  George 

Ben  Jarrett 

6% 

9/12/06 

PARTIAL  PAYMENTS   OF   PROMISSORY  NOTES 

United  States  Rule 

It  is  frequently  inconvenient  for  the  borrower  to  pay  the 
face  of  the  note  all  at  one  time.  He  is  sometimes  permitted, 
by  special  contract,  to  make  payments  at  any  time  or  at  in- 
terest bearing  periods,  until  the  note  is  paid.  These  amounts 
are  called  partial  payments  and  are  credited  on  the  back  of 
the  note,  together  with  the  date  of  payment. 

l.    For  example,  a  borrower  gives  the  following  note : 


$200.  Braddoch,  Pa.,  c/tav-.  26,  /qo6. 

dirt,  d&vyuwul,  for  value  received,  I  promise  to  pay 
tJaAYueAs  ^we^^rC^^ivc^^^c^^^^rc^^vr^^orc^^^^^v^^^^or  order, 

^W   ffundh&d  a/ncL  —t^r>c^z^^c^^r^r^^^r2^^r^CzDollars. 

100 

With  interest ;  at  6%.  /ferny   Bxow-n. 


PARTIAL   PAYMENTS   OF    PROMISSORY    NOTES       299 


The  following  payments  are 
indorsed  on  this  note  : 

What  amount  is  due  March  2, 
1908? 


Nov.  26,  1907,  $50.00. 
Jan.  2,  1908,  $25.00. 


Solution  : 


Principal 

Interest  on  $200  for  1  yr. 
The  amount  of  the  note  Nov.  20,  1907  . 
Payment  Nov.  20,  1907  ... 

Balance  =  new  principal  due  Nov.  26,  1907 


yr. 

mo. 

da 

1908 

1 

2 

1907 

11 

26 

$200.00 
12.00 

212.00 
50.00 

162.00 


Interest  on  $  1 62  for  1  mo.  6  da.    . 

Amount  due  Jan.  2,  1908 

Payment  Jan.  2,  1908   .... 

Balance  =  new  principal  due  Jan.  2,  1908 


$  .97 

162.97 
25.00 

137.97 


1908 
1908 


3        2 
1        2 


Interest  on  $  137.97  for  2  mo. 
The  amount  due  March  2,  1908 


(I 


1.38 


$  139.35 


2.  What  was  the  amount  due  on  the  note  on  Nov.  26, 
1907? 

3.  How  much  interest  was  due  Nov.  26,  1907  ?  What 
payment  was  made  ?  How  much  greater  was  the  payment 
than  the  interest  ? 

4.  How  much  was  the  new  principal  due  Nov.  26,  1907, 
after  the  payment  of  $  50.00  ? 


300  INTEREST 

5.  How  much  interest  was  due  Jan.  2,  1908?  How 
much  greater  was  the  payment  than  the  interest? 

Observe :  1.  That  the  interest  was  computed  on  the  principal  to  the 
time  of  the  first  payment ;  then  on  the  balance,  as  a  new  principal,  to  the 
time  of  the  second  payment;  then  on  the  balance,  as  a  new  principal, 
until  March  2,  1908. 

2.  That  the  interest  at  each  payment  was  first  paid  and  the  balance 
of  the  payment  was  credited  on  the  principal. 

3.  As  the  interest  must^rs^  be  paid,  in  case  the  payment  does  not  equal 
the  interest,  the  interest  must  be  computed  until  such  time  as  the  sum 
of  the  payments  equals  or  exceeds  the  interest. 

This  is  the  United  States  rule  of  partial  payments,  and  is 
the  legal  one  in  most  states. 

Find  the  amount  of  the  principal  to  the  time  of  the  first  pay- 
ment, and  from  the  amount  subtract  the  first  payment.  Con 
skier  the  remainder  as  a  new  principal  and  proceed  as  before 
until  the  time  of  final  settlement.  If  any  payment  does  not- 
equal  or  exceed  the  interest,  then  find  the  interest  to  the  time 
when  two  or  more  payments  equal  or  exceed  the  interest. 

The  Supreme  Court  of  the  United  States  has  decreed: 

(1)  That  the  payment  on  a  note  must  first  be  applied  to 
cancel  the  interest  then  due,  before  the  piincipal  may  be 
diminished. 

(2)  That  interest  must  not  be  charged  upon  interest. 

Written  Work 

1.  A  note  for  $1800,  bearing  6%  interest,  was  given 
April  1,  1903,  and  settled  Oct.  22,  1906.  On  the  back 
of  the  note  were  these  indorsements:  May  10,  1904,  $225; 
June  16,  1905,  $50;  Sept.  28,  1905,  $340;  March  10,  1906, 
$475.  Find  the  balance  due  on  the  note  at  date  of  settle- 
ment. 


PARTIAL    PAYMENTS   OF    PROMISSORY    NOTES       301 


Principal 

Interest  from  April  1,  1903  to  May  10,  190-1 

Amount  due  .May  10,  1 : * < » i 

First  payment  made  May  10,  1901  . 


l>a lance  =  new  principal  due  May  10,  1904 
Interest  from  May  10,  1901  to  June  16,  1905 


51800.00 
119.70 

1919.70 
225.00 


1694.70 


$111.85 


The  interest  exceeds  the  payment  and  a  new  principal  is  not 

formed. 
Interest  from  June  16,  1905  to  Sept.  28,  1905,  .         .    28.81 

Interest  from  May  10,  1904  to  Sept.  28,  1905  ....         140-66 

Amount  due  Sept.  28,  1905 18:35.36 

Sum  of  second  payment  June  16,  1905,  and  third  payment 

Sept.  28,  1905.  $50.00  +  8340.00  •  .  =     390.00 


Balance  =  new  principal  due  Sept.  28,  1905 
Interest  from  Sept.  28,  1905  to  March  10,  1906 
Amount  due  March  10,  1906    .... 
Fourth  payment  made  March  10, 1906     . 


Balance  =  new  principal  due  March  10,  1906  . 
Interest  from  March  10,  1906  to  Oct.  22,  1906 
Balance  due  Oct.  22,  1906        . 


1445.36 

39.024 
1484.384 
475.00 


1009.384 

37.347 

$1046.731 


2.  A  mortgage  for  $960,  bearing  6%  interest,  was  given 
June  20,  1900,  and  settled  Dec.  26,  1904.  On  the  mortgage 
wore  these  indorsements:  Nov.  2,  1901,  $140  ;  Jan.  14, 1903, 
1200;   June  1,  1904,  $30;   June  20,  1904,  $150.      Find  the 

balance  due  on  date  of  settlement. 

3.  On  a  claim  of  $850,  dated  May  2,  1901,  interest  5%, 
the  following  payments  were  made:  Aug.  8,  1901,  $200; 
Dec.  14,  1901,  $2<i0;  April  26,  1902,  $200.  How  much 
was  due  at  final  settlement  April  26,  1903? 

4.  A  note  of  $1000,  dated  Aug.  1,  1903,  bearing  interest 
at  6%,  had  the  following  payments  indorsed  upon  it: 
Dec.  20,  1903,  $250.50 ;  May  12,  1904,  $300  ;  Nov.  20,  1904, 
$400.     Find  the  amount  due  June  26,  1905. 


302 


INTEREST 


5.    June  1,  1900,  a  note  was  given  for  $1700,  with  interest 
at  6%.      The    following   payments  were   indorsed   on  this 


note 


$300. 

300. 

300. 

15. 

585. 


Dec.  1,  1900 
June  1,  1901 
Nov.  1,  1901 
April  1,  1902 
May  1,  1902 
Find  the  amount  due  July  1, 1902. 

6.  A  note  for  $240  was  made  June  1,  1903,  with  interest 
at  6  %.  The  following  indorsements  were  made  on  the  note  : 
Oct.  13, 1903,  $120  ;  Jan.  19,  1904,  $60  ;  June  1,  1904,  $60. 
Find  the  amount  due  on  the  note  Dec.  16,  1905. 

Merchants'  Rule 

When  partial  payments  are  made  on  mercantile  accounts, 
overdue,  or  on  notes  running  a  year  or  less,  the  interest  is 
often  computed  by  the  merchants'  rule. 

Find  the  amount  of  the  principal  from  the  time  it  begins  to 
hear  interest  to  the  date  of  settlement. 

Find  the  amount  of  each  payment  from  the  time  it  was  made 
to  the  date  of  settlement. 

From  the  amount  of  the  principal,  subtract  the  sum  of  the 
amounts  of  the  payments.      The  result  will  be  the  balance  due. 

Written  Work 

1.  A  note  for  $1200,  dated  July  15, 1905,  has  the  following 
indorsements:  Sept.  25,  1905,  $450;  Jan.  1,  1906,  $200; 
March  9,  1906,  $150.  How  much  is  due  July  1,  1906,  at 
6  °Jo  interest  ? 

2.  A  note  for  $2500,  dated  Jan.  1, 1907,  has  the  following 
indorsements:  Feb.  1,  1907,  $50;  March  1,  1907,  $75; 
May  1,  1907,  $100.     How  much  is  due  Oct.  1,  1907  ? 


PAET   III      EIGHTH   YEAR 

BANKS   AND   BANKING 

A  bank  is  an  institution  that  receives  and  lends  money. 
A  national  bank  may  also  issue  notes  that  circulate  as 
money. 

Anions:  the  various  forms  of  banks  in  the  United  States 
may  be  mentioned  national  banks,  which  are  under  control 
of  the  Federal  government  ;  state  banks,  which  are  under  the 
control  of  the  state ;  private  banks  ;  and  savings  banks. 

A  trust  company  is  an  institution  empowered  by  its 
charter  to  accept  and  execute  all  kinds  of  trusts,  to  act  as 
executor,  administrator,  assignee,  and  receiver.  In  most 
states  it  is  also  empowered  to  do  a  general  banking 
business. 

Savings  accounts  have  been  treated  under  the  head  of  Compound 
Interest,  as  the  computations  involved  are  a  direct  application  of  it. 

The  chief  business  of  banks  is  to  receive  deposits  for  safe 
keeping  ;  to  lend  money  on  approved  security  ;  and  to  collect 
drafts  and  bills  of  exchange. 

Discounting  notes  is  simply  lending  money  on  approved 
security. 

Opening  an  account  with  a  bank. 

When  a  person  opens  an  account  with  a  bank,  he  first  fills 
out  a  deposit  slip,  as  indicated  on  page  304,  and  gives  it.  to- 
gether with  the  deposit,  to  the  "cashier"  or  "receiving 
teller." 

303 


304 


BANKS   AND   BANKING 


DEPOSITED  WITH 

American  Rational  IBanh 

PITTSBURG,    PA. 

€tt.  ?0, 

1907 

Bills 

Dollars 

Cents 

50 

Gold 

60 

Silver 

20 

Chech  s 

ENTER    CHECKS   SEPARATELY 

/a-C  cfiat.  toaivk, 

65 

80 

ZLnuyyv  c/vu&t  @.o. 

/SO 

fO 

data  I 

325 

qo 

to  pay  a  bill  by  check,  lie  fills 
book,  similar  to  the  following  : 


Some  banks  require  the  name 
of  the  bank  on  which  the  check 
is  issued  to  be  written  on  the 
deposit  slip. 

The  depositor  then 
writes  his  name  and  ad- 
dress in  a  book  kept  by 
the  bank,  so  that  the  bank 
may  have  his  signature 
for  identification. 

He  then  receives  a  bank 
book,  which  should  always 
be  presented  to  the  teller 
when  a  deposit  is  made,  in 
order  that  the  dates  and 
amounts  of  all  the  deposits 
may  be  entered.  He  also 
receives  a  check  book,  each 
page  of  which  has  one  or 
more  blank  checks  and 
stubs.  When  he  wishes 
out  a  form  from  the  check 


Stub 

Check 

No.  /y-O/ 

Pittsburg,  Pa.,  fwn&  26,  /<?07.       No.  1^0/ 

Datefun&26;07 

American  National  Bank 

Payable  to   Qo/m 

Pay  to  the 

f\.   <=J~/vo-ynfow>i 

order  of  fo/m  ft.  3 Ivo-yyv^o-n,           f^OO.*-^- 

For  R&nt  to-  <r(ut& 

c4vn&   hurvclv&cL   and  _?£_~-^-^    -^^Do/lars. 

100 

Arn't  $<?OO.s-£ 

^.  d.  cJ'^Wi. 

BANKS   AND   BANKING  30.") 

A  check  is  a  written  order  by  a  depositor  in  a  bank,  direct- 
ing the  payment  of  money. 

The  stubs  remaining  in  a  check  book,  after  the  checks  are 
torn  out,  give  a  complete  record  of  the  checks  issued. 

1.  Who  is  the  maker  of  the  check  on  p.  304  ? 

2.  To  whose  order  is  this  check  written? 

Observe :  1.    The  maker  of  a  check  is  the  one  who  signs  the  check. 

2.    The  payee  is  the  one  to  whose  order  the  check  is  made  payable. 

:'>.  This  check  is  made  payable  to  the  order  of  John  R.  Thompson, 
which  means  that  in  order  to  receive  the  money  from  a  bank,  or  transfer 
the  check  to  another  person,  he  must  write  across  the  back  of  the  check 
the  na'mtT^John  R.  Thompson."  This  is  called  a  blank  indorsement, 
because  it  (jojeajiotstate  to  whom  the  cheek  is  made,  payable.  If  John 
R.  Thompson  should  write  across  the  hack  of  the  check  the  following  : 

Pay  to  the  order  of 
Marshall  Field  &  Co., 
Chicago,  111. 
John  R.  Thompson, 

this  would  be  known  as  a  full  indorsement,  for  no  one  but  Marshall  Field 
&  Co.  could  collect  or  indorse  the  check. 

Checks,  like  promissory  notes,  may  be  written  in  different 
ways,  as  follows : 

1.  Pay  to  bearer, 

2.  Pay  to  cash,  collectable  by  bearer. 

3.  Pay  to  James  Ogden,  or  bearer,  . 

4.  Pay  to  self  (collectable  by  maker  only). 

5.  Pay  to  the  order  of  self  (collectable  by  indorsement  of  the  maker). 

6.  Pay  to  the  order  of  James  Ogden  (collectable  by  indorsement  of 
James  Odgen  only). 

Note.  —  The  last  form  of  check  is  the  one  in  general  use. 

3.  How  may  the  check  on  p.  304  be  indorsed  in  blank  ? 

4.  How  may  it  be  indorsed  in  full  ? 

5.  Suppose  Mr.  Thompson  wishes  to  send  this  check  to 
Sage,    Allen    &    Co.,    Hartford,    Conn.,  in    payment  of    an 

HAM.    COMF1..    ARITH.— 20 


306  BANKS   AND   BANKING 

account:  first,  write  the  check  as  indorsed  by  Mr.  Thomp- 
son in  blank  ;  second,  write  the  check  as  indorsed  by  Mr. 
Thompson  in  full. 

6.  Give  reasons  why  it  will  be  better  for  Mr.  Thompson 
to  indorse  the  check  in  full. 

7.  When  a  check  is  indorsed  and  sent  by  mail,  what  form 
of  indorsement  should  always  be  used  ?     Why  ? 

8.  Give  the  essentials  of  a  check. 

Balancing  Accounts ;  Depositing  ;  Checking  on  Accounts : 

1.  Your  deposits  in  a  bank  for  the  month  of  September 
are  as  follows: 

Sept.  1,  currency,  $50;  silver,  $10;  check,  $15. 
Sept.  6,  currency,  $20;  silver,  $10  ;  check,  $100  ;  gold,  $20. 
Sept.  10,  currency,  $45;  silver,  $4.75. 
Sept.  16,  currency,  $20;  silver,  $3.40;  check,  $80. 
Sept.  25,  gold,  $40;  check,  $40;  silver,  $10. 
Sept.  29,  check,  $80;  currency,  $80;  silver,  $35. 
Make  out  deposit  slips  and  find  amount  of  deposits  for 
September. 

2.  Your  check  book  shows  the  following : 
Balance  in  bank  Sept.  1,  $847.10. 

No.  1,  Sept.  4,  Keller  Bros.,  for  coal,  $15.50. 

No.  2,  Sept.  4,  Geo.  K.  Stevenson  &  Co.,  for  groceries  for 

August,  $49.50. 
No.  3,  Sept.  4,  Dr.  S.  N.  Pool,  for  services  to  date,  $90. 
No.  4,  Sept.  5,  cash,  $55. 

No.  5,  Sept.  7,  Jos.  Home  Co.,  for  merchandise,  $65.30. 
No.  6,  Sept,  11,  Midland  Lumber  Co.,  for  lumber,  $93.75. 
No.  7,  Sept.  15,  Johnson  &  Co.,  for  repairs  on  automobile, 

$29.35. 
No.  8,  Sept.  19,  cash,  $25. 


BORROWING    FROM    HANKS  307 

No.  9,  Sept.  24,  J.   H.   McFarland,  for   interest   due   on 
note,  124. 

Write  the  checks  for  the  bills  paid  for  September,  and 
find  balance  in  bank. 

3.  Arriving  at  Chicago,  I  find  in  my  mail  a  check  from 
the  Keystone  Lumber  Co.,  Pittsburg,  Pa.,  for  $415.40,  in 
payment  of  my  salary  and  expenses  for  September.  I  wish 
to  deposit  the  same  to  my  account  in  the  Colonial  Trust  Co., 
Pittsburg,  Pa.  How  should  I  indorse  the  check  before  send- 
ing it  through  the  mail  ? 

BORROWING  FROM  BANKS  AND    COMPUTING   BANK 

DISCOUNT 

Banks  usually  lend  money  on  promissory  notes  drawn  in 
one  of  three  forms  : 

1.  The  note  is  made  payable  to  the  indorser,  who  signs  his  name  across 
the  back  of  it. 

2.  A  joint  and  several  note  is  made  payable  to  the  order  of  the  bank 
and  signed  by  both  parties  as  makers. 

3.  The  note  is  made  payable  to  the  order  of  the  bank.  The  security 
in  the  form  of  stocks,  bonds,  mortgages,  etc.,  is  deposited  as  collateral. 


$200.^.  Pittsburg,  Pa.,  ifefit.  8,  1905 

3~kx,&&  vio-nthfr  after  date J. promise  to  pay  to 

the  order  of. ft.  A  W-at&aw at  the 

Lincoln  Rational  Bank  of  Pittsburg 

Zfw-o-   f'ficncLi&cL  avid  —  -^^o^^r^r^^^c^^ryr^^^yr^Dollars 

too 

without  defalcation,  for  value  received. 

J.  &  &kandle,v. 


308  BANKS   AND   BANKING 

This  note  matures  three  months  after  Sept.  8,  or  Dec.  8.  If  the  time 
in  the  note  were  "  ninety  days  "  instead  of  "  three  months,"  the  note  would 
mature  ninety  days  after  Sept.  8,  or  Dec.  7. 

If  Mr.  Chandler  wishes  to  borrow  money  at  the  bank,  he  may  make 
out  a  note  as  on  p.  307  and  get  Mr.  Watson  to  indorse  it. 

If  both  men  are  responsible  from  a  financial  point  of  view,  the  bank 
will  buy  the  note  and  give  Mr.  Chandler  the  difference  between  the  value 
of  the  note  at  its  maturity  and  the  interest  on  that  value  at  the  legal  rate 
for  the  exact  number  of  days  the  bank  is  without  the  use  of  its  money. 

The  value  of  Mr.  Chandler's  note  is  the  amount  the  Lincoln  National 
Bank  will  receive  from  Mr.  Chandler  at  its  maturity.  If  Mr.  Chandler 
fails  to  pay.  Mr.  Watson  will  be  held  responsible. 

The  buying  of  notes  by  a  bank  is  called  discounting  notes, 
and  the  interest  deducted  is  called  bank  discount. 

The  proceeds  of  a  note  discounted  by  a  banker  or  a  broker 
is  the  value  of  the  note  at  its  maturity  less  the  discount. 

The  term  of  discount  is  the  exact  number  of  days  that 
the  borrower  has  the  use  of  the  money. 

There  are  two  methods,  however,  of  reckoning  this  term:  the  first 
method  counts  the  day  of  maturity,  but  not  the  day  of  discount;  the 
second  counts  both :  thus,  by  the  first  method  Mr.  Chandler  had 
the  use  of  the  money  22  days  in  Sept.,  31  days  in  Oct.,  30  days  in  Nov., 
and  8  days  in  Dec,  or  91  days  in  all;  by  the  second  method  he  had  the 
use  of  the  money  23  days  in  Sept.,  31  days  in  Oct.,  30  days  in  Nov.,  and 
8  days  in  Dec,  or  92  days  in  all. 

Note. — Pupils  should  solve  the  problems  according  to  the  practice 
in  their  vicinity.     Answers  are  given  for  both  methods. 

When  days  of  grace  are  allowed  they  are  included  in  the  term  of  dis- 
count, but  in  this  book  days  of  grace  are  not  reckoned. 

Computing  bank  discount  on  note  on  p.  307  : 

Date  of  maturity,  December  8. 

Term  of  discount.  91  days  (not  including  day  of  discount). 

Bank  discount  on  8200  for  91  days  at  6%  =  $3.03. 

l.  How  much  does  the  bank  pay  to  Mr.  Chandler?  How 
much  does  Mr.  Chandler  pay  to  the  bank  at  maturity?- 


BORROWING    FKo.U    BANKS 


SOP, 


•^.  If  Mr.  Chandler  had  borrowed  $200  from  Mr.  Watson 
for  3  months  at  6%,  how  much  would  he  have  paid  Mr. 
Watson  when  the  note  became  due? 

3.  How  much  would  Mr.  Chandler  have  received  from 
Mr.  Watson  at  the  time  he  borrowed  the  money? 

4.  Find  the  difference  between  the  discount  paid  to  the 
bank  and  the  interest  he  would  have  paid  to  Mr.  Watson. 

Comparative  Study 
Banks  differ  from  individuals  in  lending  money,  as  follows: 

1.  Banks  require  the  interest  on  a  note  to  be  paid  in  advance  ;  indi- 
viduals demand  interest  when  the  note  is  due,  or  annually,  if  for  a  longer 
period  than  a  year. 

2.  Banks  compute  interest  for  the  exact  number  of  days;  individuals 
compute  interest  by  months  and  years. 

3.  Banks  lend  money  for  short  periods,  usually  not  exceeding  four 
months;  individuals  lend  for  longer  periods,  not  exceeding  five  years  in 
most  states. 

4.  Banks  require  the  maker  to  give  additional  security ;  individuals 
may  or  may  not  demand  security. 

5.  Interest  is  computed  on  the  face  value  of  a  note;  bank  discount  is 
computed  on  the  value  of  a  note  at  its  maturity. 

Bank  discount  is  the  simple  interest  paid  in  advance  on  the 
value  of  a  note  at  its  maturity  for  the  exact  number  of  days 
the  banker  is  without  his  money. 

Given  the  dates  and  time  of  notes,  to  find  the  date  of 
maturity. 

Find  the  date  of  maturity  of  the  following  : 


Date 

Time 

Date 

Time 

1.  June  1 

2.  July  3 

3.  Aug.  5 

4.  Sept.  10 

2  months 
50  days 
100  days 

1  month 

5.  Jan.  2 

6.  March  3 

7.  April  1 

8.  Ma\  5 

3  months 
7~>  days 
70  days 

4  months 

810 


BANKS   AND   BANKING 


Find  the  date  of  maturity  and  the  term  of  discount. 


Date  of 

Time  of 

Date  of 

Date  of 

Time  of 

Date  of 

Note 

Note 

Discount 

Note 

Note 

Discount 

9.    March  1 

60  da. 

April  1 

14.  Jan.  2,  '08 

90  da. 

March  1 

10.    April  10 

3  mo. 

June  15 

15.  March  23 

4  mo. 

June  2 

11.   July  10 

4  mo. 

Sept.  30 

16.  Oct.  8 

60  da. 

Nov.  1 

12.    Mav  24 

30  da. 

June  1 

17.  June  5 

90  da. 

July  10 

13.    August  5 

70  da. 

Sept.  1 

18.  Sept.  24 

30  da. 

Oct.  1 

Written  Work 

1.  Write  a  promissory  note  for  $  300  payable  to  John 
Jackson,  dated  Aug.  3,  1907,  due  in  four  months,  with  inter- 
est at  6%,  and  signed  by  Glenn  Campbell. 

2.  Mr.  Jackson  indorses  the  note  in  example  1,  and  Mr. 
Campbell  borrows  the  money  from  the  Park  National  Bank. 
Indorse  the  note  in  full  and  find  the  bank  discount  and  pro- 
ceeds. 

The  following  notes  are  each  discounted  on  the  day  of 
issue.     Find  the  date  of  maturity  and  the  bank  discount. 


Date  of  Note 

Time 

Face 

Rate  of 
Discount 

3.    Aug.  10,  1906 

90  da. 

9  150 

6% 

4.   June  12,  1906 

2  mo. 

515 

6J% 

5.   July     2,  1906 

3  mo. 

1000 

u% 

6.   Jan.     8,  1906 

4  mo. 

625 

n% 

7.   Mar.     5,  1906 

50  da. 

570 

6% 

8.    May     8,  1906 

70  da. 

423.25 

5*% 

9.    Sept.    1,  1906 

1  mo. 

1200 

8J% 

10.    Dec.     1,  1906 

100  da. 

387.75 

6% 

11.    Mar.     5,  1906 

72  da. 

1125 

7% 

DISCOUNTING  NOTES  311 

Discounting  Interest  and  Non-interest  bearing  Notes. 

Business  men  frequently  take  notes  from  their  customers 
due  at  a  future  date,  and  in  case  they  need  the  money  before 
the  notes  become  due,  they  sell  them  to  a  bank.  The  bank 
deducts  from  the  value  of  each  note  at  maturity  the  interest 
(bank  discount)  for  the  term  of  discount.  These  notes  may 
or  may  not  bear  interest.     • 

Mr.  James  Edwards  has  two  notes  that  read  as  follows : 


$<?0.^  Columbus,  Ohio,  7n<M*A  2,  1907 

3/i%&&  vu>nth&  after  date J. promise  to  pay  to 

the  order  of  <^^ryr*^r^^j!am-&a,  £dnAXMj£&c^^c^r^c^^>- 
c/tinetu  and  i^^^^r^^o^^o^^c^^^r^^c^^rC^Z>oZZa;»5. 

'  100 

Value  received. 

ff&nvy  (ZmaXaav. 


$/50^-  Columbus,  Ohio,  ?11awA  fO,  1907 


100 


&ouv  iyYuy)ith&  after  date J. promise  to  pay  to 

the  order  of^^yr^c^y^yc^^a-'viv&a,  €dwavcU,-c^?^<r?crr^ry?^^'- 
€n&  f^vAvdv&d  S^viUf  and  —*^^^y^^cY>?^c^^I)ollars. 

Value  received,  with  interest  at  6%. 


312  BANKS   AND   BANKING 

1.  What  is  the  value  of  the  first  note  at  maturity? 

2.  What  is  the  value  of  the  second  note  at  maturity? 

3.  Mr.  Edwards  gets  both  notes  discounted  April  20, 
1907,  at  6  %.  Why  is  the  discount  on  the  first  note  computed 
on  $90?    on  the  second  note,  on  $153? 

Banks  always  discount  notes  on  the  amount  they  are  to 
receive  at  maturity. 

Discounting  the  first  note  on  page  311 : 

Maturity  of  note,  June  2. 

Value  of  the  note  at  maturity     .     .     .  =  $90.00,  or  face 

Bank  Discount  for  43  da.  at  6  %      .     .  =         .65 

Proceeds  April  20 =  9  89.35 

Discounting  the  second  note  on  page  311: 

Maturity  of  note,  July  10. 

Value  of  the  note  at  maturity    =  %  153.00  ox  face  +  interest  for  4  months. 

Bank  Discount  for  81  da,  at  6%  =        2.07 

Proceeds  April  20      ....=$  150.93 

Written  Work 

1.  A  60-day  note  for  $2500,  without  interest,  dated  Jan. 
12,  1907,  was  discounted  Feb.  12,  1907.  Find  the  proceeds 
of  this  note. 

2.  Find  the  proceeds  of  a  90-day  note  for  $1560,  with 
interest  at  6  %,  dated  March  8,  and  discounted  April  12. 

3.  Find  the  proceeds  of  the  note  in  example  2  without 
interest. 

4.  A  90-day  note  for  $  4500,  with  interest  at  6  %,  is  dis- 
counted 30  days  after  date.     Find  the  proceeds. 

Suggestion.  —  Note  the  difference  between  a  note  for  90  days  and  a 
note  discounted  for  90  days. 


DISCOUNTING  NOTES  313 

5.  Find  the  proceeds  of  the  note  in  example  4  without 
interest. 

6.  A  120-day  note  for  $3500,  without  interest,  dated 
June  5,  is  discounted  Aug.  10.     Find  the  proceeds. 

7.  Find  the  proceeds  in  the  note  of  example  6,  if  the  note 
bears  interest  at  6  %. 

8.  The  proceeds  of  a  90-day  note,  without  interest,  dis- 
counted 30  days  after  date,  is  $  990.     Find  the  face. 

9.  A  note  for  $1200,  bearing  interest  for  3  mo.  at  6  %, 
was  dated  Jan.  15  and  discounted  Feb.  20.  Find  the 
proceeds. 

10.  Mr.  Boyd  gives  his  note  Jan.  10,  1905,  to  William 
Savers  for  $200,  payable  in  9  months,  with  interest  at  6%. 
What  is  Mr.  Boyd's  note  worth  on  the  day  of  issue?  on 
the  day  of  maturity  ? 

11.  Should  Mr.  Boyd  get  the  note  discounted  July  5, 
on  how  much  money  would  the  bank  reckon  the  discount  ? 

12.  Find  the  amount  Mr.  Boyd  would  receive  July  5. 
What  is  the  money  received  by  Mr.  Boyd  called  with  ref- 
erence to  the  note  ? 

13.  Write  the  note  given  by  Mr.  Sanders  and  transfer  it 
by  indorsement  in  full  to  one  of  your  local  banks. 

14.  Face,  $223.50  ;  time,  90  days ;  rate  of  interest,  6%  ;  term 
of  discount,  50  days;  rate  of  discount,  8%.     Find  proceeds. 

15.  A  business  man's  bank  account  is  overdrawn  ^381.50, 
and  he  presents  to  the  bank,  May  1,  two  notes  to  be  dis- 
counted, at  6%,  and  the  proceeds  to  be  placed  to  his  credit. 

Face  Date  Time  Rate  of  Interest 

$290         Mar.  10  5  mo.  Without  interest 

$355         Apr.  20  90  da.  6% 

Find  his  balance. 


314  BANKS   AND   BANKING 

16.  The  discount  on  a  note  for  $400  for  60  days,  exact 
time,  is  $6.00.     Find  the  rate  of  discount. 

17.  A  broker  buys  a  $300  note,  thirty  days  before  matu- 
rity, for  $297.     Find  the  rate  of  discount. 

18.  Mr.  James  sold  a  horse  for  $155,  and  took  the  pur- 
chaser's note,  dated  Jan.  20,  1905,  due  in  one  year,  with 
interest  at  4|  %.  Mr.  James  sold  the  note  to  the  Farmers' 
Bank,  Oct.  10,  at  7  %  discount.     How  much  did  he  realize  ? 

19.  A  note  for  $1800,  at  8%,  dated  August  1,  due  in  3 
months,  was  discounted  October  6,  at  6  °J0  •    Find  the  proceeds. 

20.  What  should  the  Merchants'  National  Bank  pay  for  a 
note  of  $1200,  bearing  &%  interest,  dated  April  12,  due  in 
4  months,  if  purchased  June  1,  at  6  %  discount  ? 

21.  What  are  the  proceeds  of  a  note  for  $2500,  dated 
February  10,  1907,  and  due  in  4  months,  without  interest, 
if  discounted  March  24,  at  6  %  ? 

22.  A  merchant's  bank  book  shows  a  balance  of  $1375.50, 
and  he  presents  at  the  bank  four  notes,  which  are  discounted 
June  1,  at  6  %,  and  the  proceeds  placed  to  his  credit : 

Face  Date 

$600  March  4 

$1375  April  2 

$1050  March  19 

$2000  May  29 

Find  his  balance  in  bank  then. 

23.  For  how  much  must  I  give  my  note,  discounted  at  a 
bank  for  60  days,  at  6%,  to  realize  $990  ? 

Note.  —  The  proceeds  of  $1,  discounted  for  60  days,  at  6%  =  $.99. 

24.  For  what  sum  must  I  draw  my  note  so  that  when  dis- 
counted at  6%  for  90  days  I  may  realize  $2758? 


Time 

Rate  of  Interest 

90  days 

6% 

4  months 

No  interest 

90  days 

5% 

3  mo. 

No  interest 

EXCHANGE 

Paying  Bills  at  a  Distance 

What  is  meant  by  a  debtor?  by  a  creditor?  How  may  a 
debtor  pay  a  bill  in  a  distant  city  without  the  actual  transfer 
of  cash  ?  How  may  a  creditor  collect  a  bill  in  a  distant  city 
without  the  actual  transfer  of  cash  ? 

Exchange  is  a  method  of  paying  or  collecting  bills  at  a 
distance  without  the  actual  transfer  of  money. 

There  are  several  different  ways  in  which  bills  may  be  paid 
at  a  distance  without  the  transmission  of  money: 

(1)  By  a  postal  money  order. 

(2)  By  an  express  money  order. 

(3)  By  a  telegraphic  money  order. 

(4)  By  a  personal  check. 

(5)  By  a  bank  draft  (banker's  check). 

Paying  by  postal  or  express  money  order. 

If  you  wish  to  order  from  Siegel,  Cooper  &  Co..  Chicago,  $15  worth  of 
merchandise,  unless  you  have  credit  there,  you  will  probably  send  them 
(1)  either  a  postal  money  order,  or  (2)  an  express  money  order.  The 
first  will  direct  the  postmaster  at  Chicago,  the  second  some  express  agent 
at  Chicago,  to  pay  to  the  order  of  Siegel.  Cooper  &  Co.  i  15. 

The  cost  of  either  of  the  above  orders  is  the  same ;  the  only  differ- 
ence being  that  a  postal  money  order  is  payable  to  the  order  of  the 
party  or  firm  upon  identification  at  the  place  named  in  the  order,  while 
an  express  money  order  is  payable  to  the  party  or  tirin  upon  identifica- 
tion at  any  office  of  the  same  company  where  orders  are  sold. 

3 1 5 


31G  EXCHANGE 

Money  orders  may  be  purchased  for  any  amount  up  to  $100,  payable 
to  any  person  or  firm  in  the  United  States,  or  foreign  countries  where 
such  orders  are  sold. 

The  rates  charged  'in  the  United  States  are  as  follows  : 

$2.50  and  under 3? 


5? 

8? 
10? 
12? 
15? 
18  ? 
20? 
25  (» 
30? 


Over    $2.50  and  not  exceeding  $5.00  . 

Over    $5.00  and  not  exceeding  $10.00  . 

Over  $  10.00  and  not  exceeding  $20.00  . 

Over  $20.00  and  not  exceeding  $30.00  . 

Over  $30.00  and  not  exceeding  $40.00  . 

Over  $10.00  and  not  exceeding  $  50.00  . 

Over  $50.00  and  not  exceeding  $  60.00  . 

Over  $60.00  and  not  exceeding  $75.00  . 
Over  $75.00  and  not  exceeding  $  100.00  . 

The  rates  to  foreign  countries  are  from  10  ?  to  $  1  for  the  same 
amounts  as  domestic  orders. 

This  fee  of  from  3  ?  to  30?  for  domestic  orders,  and  from  10?  to  $  1 
for  foreign  orders,  to  cover  the  cost  of  paying  the  bills  at  a  distance, 
is  called  the  exchange  for  issuing  the  orders. 

Paying  by  telegraphic  money  order. 

Such  orders  are  drawn  by  agents  of  the  telegraph  company,  and 
direct  the  agent  at  some  designated  office  to  pay  to  the  person  named  in 
the  telegraphic  message,  upon  identification,  the  sum  specified. 

Th3  present  rates  for  sending  money  by  telegraphic  order  are  as  follows : 

For  $25  or  less,  double  the  cost  of  a  ten-word  message,  plus  25  ?. 

Above  $  25,  double  the  cost  of  a  ten- word  message,  plus  1  %  of  the 
amount  of  the  order. 

Paying  by  checks. 

Business  men  find  it  necessary  to  pay  bills  in  their  vicinity  or  at  a 
distance,  almost  daily,  and  if  their  financial  standing  is  good,  their  checks 
are  generally  accepted  in  payment.  In  fact,  most  bills  to-day  are  paid 
by  checks. 

Sometimes  the  seller  does  not  know  the  financial  standing  of  the  pur- 
chaser, and  therefore  requires  the  check  accompanying  the  order  to  be 
certified ;  that  is,  the  cashier  of  the  bank  on  which  the  check  is  drawn 
stamps  the  word  "  certified,"  with  the  date  and  his  signature,  across  the 
face  of  the  check.  The  check  is  thereafter  the  check  of  the  bank,  and 
is  good  as  long  as  the  bank  is  solvent. 


EXCHANGE  317 

A  certified  check  is  a  notice  to  the  payee  of  the  check  that 
the  amount  named  on  the  face  has  been  taken  from  the 
maker's  deposit  and  placed  with  the  bank's  funds  for  the 
payment  of  the  check  when  presented. 

Certified  checks  are  frequently  demanded  in  payment  of  notes  and 
collections  at  banks,  and  in  payments  where  the  payee  does  not  wish  fco 
take  a  personal  check.  Like  other  checks,  they  are  mailed  daily  in 
payment  of  bills  in  all  parts  of  the  country. 

1.  What  is  a  check?     What  are  the  essentials  of  a  check? 

2.  In  buying  a  lot  from  James  Carothers  for  $800,  you  are 
asked  to  give  your  certified  check  for  the  amount.  Write  the 
check  on  your  local  bank,  yourself  being  the  maker. 

3.  Moore  &  Co.,  Youngstown,  Ohio,  purchase  'IB 825  worth 

of  furniture  at  20%  and  10%  off  from  James  Boydson  &  Co., 

Detroit,  Mich.,  3%  off  for  cash  in  10  days.     They  send  a 

certified  check  within  ten  days  on  the  Diamond  Trust  Co., 

of  which  James  Patterson  is  secretary  and  treasurer.     Write 

the  certified  check  in  payment  of  the  bill. 

Note.  —  The  secretary  and  treasurer  of  a  trust  company  corresponds 
to  the  cashier  of  a  bank. 

4.  William  Anderson,  7531  Hermitage  Ave.,  Chicago,  111., 

receives  a  check  on  the   First   National  Bank  of   Wilkins- 

burg,  Pa.,  from  Freeman  Lewis  for  $730.80  in  settlement 

of  an  estate.     The  Commercial  National  Bank  of  Chicago 

charges  Mr.  Anderson  $1.50  for  collecting  the  check.     This 

fee  is  called  the  exchange  for  collecting. 

A  person  who  cashes  a  check  at  a  bank  in  which  he  is  not  a  depositor 
is  frequently  charged  an  exchange  of  10^  and  upward,  according  to  the 
amount  of  the  check. 

Paying  by  bank  draft. 

A  draft  is  a  check  drawn  by  one  bank  on  another. 

As  New  York  City  and  Chicago  banks  collect  exchange 

on  outside  checks,  nearly  all  banks   keep  deposits   there,  as 


318 


EXCHANGE 


well  as  in  most  of  the  other  large  commercial  centers,  to 
accommodate  their  depositors  and  others,  who  have  occasion 
to  remit  payment  for  bills  in  any  part  of  the  country. 

Bauks  usually  charge  exchange  on  drafts  to  cover  the  cost  of  keeping 
funds  on  deposit  at  these  commercial  centers.  This  fee  varies  from  -^% 
to  \%  of  the  face.  When  the  draft  is  less  than  $100,  a  fixed  charge  is 
frequently  made,  varying  from  10  f   to  50^. 

The  custom  of  banks  is  not  to  charge  depositors  for  drafts. 

In  issuing  or  collecting  a  draft,  the  exchange  is  either  a 
fee  or  a  certain  per  cent  of  the  face  of  the  draft. 

New  York  and  Chicago  drafts  are  usually  cashed  at  any  point  in  the 
United  States  without  exchange.  Drafts  on  other  large  cities  are  cashed 
without  exchange  in  the  territory  contiguous  to  those  cities. 

Brown  &  Foster,  Cleveland,  O.,  buy  $2500  worth  of 
merchandise  from  John  Wanamaker  &  Co.,  New  York ;  and 
$650  worth  of  machines  from  the  Wheeler  Wilson  Co., 
Bridgeport,  Conn.  The  business  method  of  paying  these 
bills  is  either  by  a  check  or  by  a  bank  draft.  The  draft  is 
made  payable  to  the  order  of  the  purchaser,  who  indorses  it 
in  full  to  the  payee.     For  example  : 


Cleveland  National  Bank 

Cleveland,  Ohio-  ^we  2,  1097 ,  ;ya  /o^-O 

Pay  to  tlie  order  of  Bvowi,  V  dfaat&v $2600^. 

3w-&nty-(vv-E,  /runoU&d  V  —  -c^^c^^c^^r^vyc^DoUaj^s. 

To  (Efje  iJHercanttle  National  Bank, 

New  York,  JV*.  Y. 

d.  ?Vl.  /MwveA,.. 

Cashier. 


EXCHANGE  :;i'.t 

This  draft  simply  means  that  Brown  &  Foster  purchased  at  the  bank 
where  they  kept  their  deposit  a  draft  (banker's  check)  for  the  above 
amount.  The  Cleveland  National  Bank  had  money  on  deposit  at  the 
Mercantile  National  Bank,  and  simply  checked  on  its  deposit.  Had 
Brown  &  Foster  not  been  depositors  in  the  Cleveland  National  Bank, 
they  would  probably  have  been  charged  T\%  exchange.  The  draft 
would  then  have  cost  them  $2502.50. 

The  party  who  signs  a  draft  is  called  the  drawer  of  a 
draft. 

The  party  to  whose  order  the  draft  is  drawn  is  called  the 
payee  of  the  draft. 

The  party  who  is  to  pay  the  money  is  called  the  drawee  of 

the  draft. 

Thus,  in  the  draft  on  p.  318,  the  cashier  of  the  Cleveland  National 
Bank  is  the  drawer;  Brown  &  Foster  the  payee;  and  The  Mercantile 
National  Bank  the  drawee. 

Written  Work 

1.  Find  the  cost  of  a  New  York  draft  for  $550.25  at  ^  % 
exchange. 

2.  Mr.  Amidon  buys  $2500  worth  of  farm  implements  at 
30%  and  10%  off,  and  pays  by  a  Chicago  draft  at  \%  ex- 
change.    Find  the  face  of  the  draft  and  the  exchange. 

3.  Find  the  cost  of  sending  $80  from  Pittsburg  to  Chi- 
cago by  telegraphic  money  order,  the  rate  being  25  f  for 
10  words. 

4.  I  sent  $75.80  to  Chicago  by  express  money  order.  How 
much  could  I  have  saved  by  purchasing  a  bank  draft  at  15 
cents  exchange  ? 

5.  A  draft  costs  $1080,  including  the  exchange  at  ^%. 
Find  the  face. 

Suggestion.  —  $  1080  is  100^%  of  the  face. 


320  EXCHANGE 

6.  Write  a  draft  for  $2600,  making'  one  of  your  local 
banks  the  drawer,  the  First  National  Bank  of  Buffalo,  N.Y., 
the  payee,  and  the  Niagara  Falls  Power  Co.  the  drawee. 
Indorse  the  draft  in  full  to  James  Osborne  &  Co.,  Syra- 
cuse, N.Y. 

7.  Mr.  Madison  had  a  note  for  81000  discounted  for  60 
days  at  6%,  and  with  the  proceeds  bought  a  Chicago  draft 
at  yo%  exchange,  which  he  mailed  to  Mandel  Bros.,  Chicago, 
to  apply  on  account.  Find  the  face  of  the  draft  and  the  cost 
of  exchange. 

8.  My  settlement  of  an  account  in  New  Orleans  gives 
me  $26785.50.  After  investing  #13750  of  this  amount  in 
a  land  deal  on  which  I  pay  my  agent  2%  commission,  I  pur- 
chase a  New  York  draft  with  the  balance  at  ^%  exchange. 
Find  the  exchange,  the  commission,  and  the  face  of  the 
draft. 

9.  James  Anderson  &  Son,  Helena,  Montana,  order  $790 
worth  of  goods  from  a  Boston  firm,  and  send  in  payment  a 
New  York  draft  at  \  %  exchange.  Find  the  cost  of  the 
draft. 

10.  A  dealer  in  San  Francisco  buys  $2000  worth  of  goods 
at  30%  and  10%  off  and  sells  them  at  an  advance  of  25% 
on  the  cash  price.  After  paying  for  these  goods  with  a 
Chicago  draft  at  \  %  exchange,  find  his  profit. 

Collecting  Bills  at  a  Distance 

Bills  are  collected  at  a  distance  in  two  ways : 

(1)  By  a  sight  commercial  draft  of  a  creditor  on  a  debtor. 

(2)  By  a  time  commercial  draft  of  a  creditor  on  a  debtor. 

Bills  collected  by  a  sight  commercial  draft. 

Tf  Letche  &  Co.,  grain  dealers,  Pittsburg,  Pa.,  order  from  Harris 
Bros.,  Chicago,   111.,    1    car   load   of  No.  1  oats,  Harris  Bros,  will  ship 


EXCHANGE  321 

the  car  load  of  oats  to  Pittsburg  to  tlic  order  of  themselves  and  draw 
a  sight  draft  on  Letche  &  Co.,  payable  to  the  order  of  some  Chicago 
bank,  and  deposit  it  with  the  bill  of  lading  for  collection.  The  Chicago 
bank  will  then  mail  the  draft,  together  with  the  bill  of  lading,  to  some 
bank  in  Pittsburg.  The  Pittsburg  bank  will  notify  Letche  &  Co.  If 
the  car  load  of  oats  is  accepted  by  Letche  &  Co.,  they  will  pay  the  draft 
and  receive  the  bill  of  lading  which  will  entitle  them  to  the  oats. 

This  form  of  draft  is  commonly  known  as  a  commercial 
sight  draft  and  reads  as  follows : 


$^0^.  Chicago,  III.,  fusne,  27,  1906 

~Cy^yC^C^yC^C^^Clt  av^/ito^yr^^^^^^^y^yc^c^-JPay  to 

the  order  of /at  oAatio-na.1  Bank,  <&,Aie-aao, 

Sow,  /funded  <$£fty  V  ^y^^^^os^c^DoUars- 
J'al//r  received,  and  charge  to  account  of 

To  JUUAe,  V  &».  )  ,         •     n 

L  Zi-aAsVva,  Jovoa-., 

No.   /#■  &ltt&6-Ul<p,    <Pa.      )  Chicago,  III. 


A  bill  of  lading  is  a  receipt  given  by  the  carrier  to  the 
shipper.  The  goods  shipped  and  their  value  are  described 
on  its  face,  and  on  the  back  of  the  receipt  is  stated  the 
contract  of  shipment. 

In  case  Letche  &  Co.  refused  to  accept  the  oats,  the  draft  would  be 
returned  to  the  Chicago  bank,  which  in  turn  would  notify  Harris  Bros. 

Creditors  use  sight  drafts  in  the  collection  of  debts  due  or 
past  due. 

Bills  collected  by  a  time  commercial  draft. 

Often  a  draft  reads  '••'!()  to  90  days  after  sight."  Such  a  draft  is 
called  a  time  commercial  draft. 

HAM.     COMPL.     AIM  I  II.  — 21 


322  EXCHANGE 

The  method  of  collecting  by  a  time  commercial  draft  is  as  follows : 


$/200^  Pittsburg,    Pa.,  fun&  27,  1006 

^v?cZu  Gbxufr  aft&v  octant Pay  to 

tJie  order  of JClk&iVu  cftatuyyuxl  Bowk, 

cfu<-&£/v-&  fi-wyictv&cL  and  —  rrrrrrrr^rcccccc^yy^i'rrrrrLDoUars. 

100 

Value  received,  and  charge  to  account  of 

To  She,  (Z&YYI&  Buqqu  &&.,    )   n       .        „„  ^ 

7//  y  favdan,  V  Ola., 

No.   /32 ,      €-ln&Lnnatv.    €..     )  Pittsburg,    Pa. 


The  Cincinnati  bank  to  which  this  draft  is  mailed  immediately  notifies 
the  Acme  Buggy  Co.  and  if  the  Company  agrees  to  pay  the  draft,  when 
due,  the  following  is  written  across  the  face  of  it : 

"  Accepted 
Date 

Acme  Buggy  Co." 

If  the  Company  refuses  to  accept  the  draft,  the  Cincinnati  bank  will 
return  it  to  the  Liberty  National  Bank,  and  Jordan  &  Co.  will  be  notified 
that  the  goods  are  at  Cincinnati  at  their  risk. 

The  term  of  discount  in  a  draft  payable  "  after  sight "  begins  to  run 
from  the  date  of  acceptance ;  in  a  draft  payable  after  date,  from  the  date 
of  the  draft. 

In  collecting  by  draft,  the  exchange  is  always  collected  on  the  face, 
not  on  the  proceeds,  of  the  draft. 

Written  Work 

1.  If  the  draft  of  Jordan  &  Co.  was  accepted  and  dis- 
counted June  29,  1906,  find  the  term  of  discount.    ' 

2.  Find  the  proceeds  remitted  to  Jordan  &  Co.  if  this 
draft  was  discounted  June  29  at  7  %,  with  |  o/0  exchange  for 
collecting. 


EXCHANGE  323 

3.  The  Jareki  Mfg.  Co.,  Sandusky,  O.,  draw  at  sight  on 
James  Howard,  Canonsburg,  Pa.,  for  $159.70  through  the 
Erie  National  Bank,  Sandusky,  O.      Write  the  draft. 

4.  Freeman  Bros.,  Fargo,  N.D.,  Jan.  2,  1907,  sell  on 
60  days'  time  to  the  Standard  Milling  Co.,  Minneapolis, 
Minn.,  12000  bu.  No.  2  wheat  at  92|^  per  bu.,  delivered 
at  Minneapolis,  and  draw  a  time  draft  which  is  accepted  by 
the  Standard  Milling  Co.  The  Merchants  National  Bank  of 
Minneapolis  buys  this  draft  Feb.  1,  1907,  at  7  %  discount. 
If  exchange  is  \%,  rind  the  proceeds  from  the  sale  of  the 
wheat. 

5.  Charles  Boyd,  Fremont,  O.,  owes  Samuel  Johnson, 
Jacksonville  111.,  1600  due  June  10.  1907.  Mr.  Johnson 
desires  the  money  immediately,  and  draws  on  Mr.  Boyd 
March  24,  1907,  through  the  Illinois  National  Bank,  Jack- 
sonville, a  time  draft  due  June  10,  which  Mr.  Boyd  accepts 
March  30.  The  Fremont  bank  discounts  the  draft  at  6% 
on  the  day  of  acceptance.  If  the  exchange  is  \°Jo->  how  much 
is  remitted  to  Mr.  Johnson  ? 

6.  T.  F.  Bowman  &  Co.,  Chicago,  sell  to  Speer  Bros., 
Seattle,  Wash.,  $4000  worth  of  merchandise.  Terms:  60 
days  net;  6%  off  30  days.  Write  the  banker's  check 
given  by  the  Seattle  National  Bank  and  indorsed  in  full  by 
T.  F.  Bowman  &  Co.  Find  the  cost  of  the  banker's  check 
at  I  %  exchange,  if  paid  within  30  days. 

7.  James  Brown,  Lansing,  Mich.,  sells  $2500  worth  of 
celery  on  March  1,  1908.  to  Grimm  Bros.,  Boston,  Mass., 
and  draws  a  draft  for  90  days  after  sight.  The  draft  is 
accepted  March  18,  and  discounted  the  same  day  at  6%. 
If  the  cost  of  collection  is  \  %  exchange,  find  the  proceeds 
from  the  sale  of  the  celery. 


STOCKS   AND   BONDS 

STOCKS 

When  an  individual  or  a  few  persons  do  not  wish  to  fur- 
nish all  the  capital  or  money  required  for  a  business,  or  to 
assume  all  the  responsibility,  they  may  secure  a  charter  from 
the  state  government  to  form  a  corporation  or  stock  com- 
pany, and  choose  a  board  of  directors  to  transact  the  busi- 
ness in  the  name  of  the  firm  designated  in  their  charter. 

A  corporation  is  a  company  authorized  by  a  charter  to 
transact  business  as  an  individual. 

The  capital  stock  of  a  company  is  the  amount  of  stock 
for  which  shares  are  issued.  Thus,  1000  shares  at  $10  each 
make  a  capitalization  of  $10000. 

The  par  value  of  the  shares  in  different  corporations  varies  from  %  1 
to  %  100.  The  persons  who  form  the  corporation  determine  the  number 
and  par  value  of  the  shares.  Observe  that  the  certificate  on  p.  325 
gives  the  number  and  value  of  the  shares. 

The  par  value  of  a  share  of  stock  is  the  amount  written  on 
the  face  of  the  stock  certificate. 

What  is  the  par  value  of  the  stock  certificate  on  p.  325  ? 

The  market  value  of  a  stock  is  the  price  at  which  it  is 
selling. 

A  stock  is  selling  at  a  discount  when  purchased  for  less  than  its  pai 
value,  and  at  a  premium  when  selling  for  more  than  its  par  value. 

324 


STOCKS  325 


STOCK   CERTIFICATE 
Incorporated  under  the  Laws  of  the  State  of  Pennsylvania 


<yfi>.    2  < 


20  tf/iat&fr 


Enorpcnocnt  Iron  OTompang  of  pttsimrg 

This  certifies  that j/oont&o,  W-oo-cL is  the  owner 

of. Sw-tnty full  paid  shares 

of  the  Capital  Stock  of  One  Hundred  Dollars  each  of  the 
Independent  Iron  Company. 

Transferable  only  on  the  books  of  the  Company  by 
the  holder  in  person  or  by  an  attorney  upon  the  surrender 

of  this  certificate. 

j.  &.  711&I/&I,  President. 

B.  c/1  #W£A,  Secretary. 
Pittsburg  June  1,  1906. 


A  stockholder  is  one  who  holds  stock  in  a  corporation. 

An  assessment  is  a  sum  levied  on  the  par  value  of  each 
share  of  stock  to  defray  expenses  and  losses  when  the  earn- 
ings are  not  sufficient. 

A  dividend  is  a  part  of  the  net  profits  divided  among 
the  stockholders,  in  proportion  to  the  par  value  of  their 
stock.  These  dividends  are  paid  yearly,  half-yearly,  or 
quarterly,  as  the  board  of  directors  may  determine. 

A  stock  broker  is  a  person  who  buys  and  sells  stocks  for 
another.  The  charge,  called  brokerage,  is  usually  \  %  to  \  % 
on  a  par  value  of  a  hundred  dollars.  Most  brokers  belong  to 
some  stock  exchange. 


326  STOCKS   AND  BONDS 

Par  Value  and  Brokerage. 

1.  Mr.  James  buys  10  shares  of  railroad  stock,  par  value 
$100  per  share,  at  $89  per  share,  brokerage  ^%. 

1.  What  is  the  par  value  of  each  share? 

2.  What  is  the  market  value  of  each  share? 

3.  Show  that  each  share  costs  Mr.  James  $  89.12J. 

In  the  study  of  this  subject  the  following  should  always 
be  observed  : 

1.  When  the  par  value  of  a  stock  is  not  stated  it  is  always  regarded 
as  |100. 

2.  When  a  stock  is  quoted  at  90,  110,  78,  etc.,  it  always  means  so 
many  %  of  the  par  value.  A  stock  quoted  above  100  is  said  to  be  above 
par,  or  at  a  premium,  and  one  quoted  below  100,  below  par,  or  at  a  discount. 

3.  Brokerage  is  always  reckoned  on  the  par  value  and  the  broker 
collects  brokerage  from  both  the  buyer  and  the  seller.  \°/0  brokerage 
means  $.12^  on  a  par  value  of  $100,  or  $.06£  on  a  par  value  of  $ 50. 

To  find  the  cost  we  add  the  brokerage  to  the  selling  price  or  pur- 
chase price  and  then  multiply  that  amount  by  the  number  of  shares 
bought  or  sold.  Brokerage  is  not  to  be  computed,_unless  stated  in  the 
problem. 

Written  Work 

1.  Find  the  cost  of  48  shares  of  railroad  stock  bought  at 
95,  brokerage  \  %  • 

$95  +  $  \  =  |9oi  =  cost  of  1  share. 

48  x  $95£  =  14566,  cost  of  48  shares. 

Find  the  cost  of : 

2.  60  shares  of  stock  at  101,  brokerage  |  %. 

3.  88  shares  of  stock  at  102,  brokerage  \°Jo- 

4.  104  shares  of  bank  stock  at  116J,  brokerage  \  %. 

5.  120  shares  railroad  stock  at  94|,  brokerage  \  %  • 


STOCKS  327 

6.  My  broker  sold  for  me  128  shares  of  mining  stock  at 
156,  brokerage  |%.      What  sum  should  I  receive? 

Find  the  net  amount  received  from  the  sale  of  the  follow- 
ing, including  brokerage  at  \o/0  : 

7.  125  shares  at  09|.  9.    500  shares  at  132|. 

8.  145  shares  at  142|.  10.    1000  shares  at  37|. 

11.  I  bought  125  shares  of  Penn.  R.  R.  stock  at  123|  and 
sold  it  at  129|;  brokerage  |%.     Find  the  net  gain. 

$  129f  -  %\  =  $129.25,  amount  realized  from  each  share 
$  123J  +  $  I  =  $123.625,  cost  of  each  share 
$5,625,  gain  on  each  share 
125  x  $5,625  =  $703.13,  net  gain 

Why  do  we  subtract  the  brokerage  when  selling  stock? 
Why  do  we  add  the  brokerage  when  buying  stock  ? 

12.  How  many  shares  of  railroad  stock  at  108 1,  brokerage 
l  %,  can  be  purchased  for  $26100  ? 

13.  How  many  shares  of  stock  must  be  sold  at  99|>  brok- 
erage |  %,  to  pay  a  debt  of  $793  ? 

14.  I  receive  $1375  net  profits  on  stock  bought  at  58  and 

sold  at  72,  brokerage  ^  %  in  each  case.     Find  the  number  of 

shares. 

15.  If  I  realized  $1595  net  from  the  sale  of  stock,  broker- 
age |  %,  rind  the  number  of  shares  sold  at  $40  per  share. 

16.  How  many  shares  of  stock  selling  at  $45  per  share, 
brokerage  \  %,  can  be  purchased  for  $2000  ?  (Parts  of  a  share 
are  not  sold.) 

17.  A  note  for  $5000,  with  interest  at  6  %,  was  paid  1  year 
4  months  and  18  days  after  date  and  the  amount  invested  in 
stock  at  87|.     Find  the  number  of  shares  purchased. 


328  STOCKS  AND   BONDS 

Premium  and  Discount. 

1.  What  is  the  cost  of  1  share  of  stock,  par  value  $100, 
selling  at  10  %  discount  ?  at  40  %  premium  ?  at  30  %  discount  ? 

2.  What  is  the  cost  of  60  shares  of  bank  stock,  par  value 
$50,  at  5%  premium,  brokerage  \  %  ? 

Par  value  of  1  share   =  $50. 

Premium  of  1  share    =  .05  x  $50  =  $2.50. 

Brokerage  on  1  share  =  .00^  x  $50  =  $  A2\. 

Cost  of  1  share  =  $50.  +  $2.50  +  $.12|,  or  $52.62£. 
Cost  of  60  shares  =  60  x  $52.62|  =  $3157.50. 

Note.  —  All  premiums  are  reckoned  on,  and  added  to,  the  par  value; 
and  all  discounts  are  reckoned  on,  and  subtracted  from,  the  par   value. 

Find  the  cost  of  the  following  stock,  brokerage  ^  %  : 

3.  16  shares,  par  value  $50,  at  3%  premium. 

4.  42  shares,  par  value  $50,  at  10%  discount. 

5.  100  shares,  par  value  $25,  at  14  %  discount. 

6.  220  shares,  par  value  $100,  at  \  %  premium. 

7.  150  shares,  par  value  $50,  at  f  %  discount. 

8.  My  broker  purchased  for  me  256  shares  of  milling 
stock,  par  value  100,  at  4-|-%  premium,  brokerage  \°/0. 
How  much  did  the  stock  cost  me  ? 

9.  How  much  will  120  shares  of  railroad  stock  cost  at 
114f ,  brokerage  |  %  ? 

10.  How  much  is  realized  from  the  sale  of  480  shares  of 
gas  stock,  par  value  $50,  at  2%  discount,  brokerage  \°Jo  ? 

11.  How  many  shares  of  stock  can  be  bought  for  $2475, 

at  3  %  premium,  brokerage  \  %  ? 

Par  value  of  1  share  =  $  100 
Premium  on  1  share  =  $     3. 
Brokerage  on  1  share  =  $        .125 
Entire  cost  of  1  share  =  $  103.125 
$  24750  -  $  103.125  =  240,  number  of  shares 


STOCKS  320 

Find  the  number  of  shares  bought  for  : 

12.  $5827.50,  par  value  $50,  at  3%  discount,  brokerage 

Wo- 

13.  $11970,  at  106|,  brokerage  |%. 

14.  $  2165,  par  value  $  50,  at  8%  premium,  brokerage  \%. 

15.  $  19677,  at  116|,  brokerage  \%. 

16.  $10025,  par  value  $50,  brokerage  \  %. 

Dividends  and  Investments. 

1.  What  is  the  income  from  $  1000  loaned  for  1  year  at 
6%? 

2.  What  is  the  income  from  $  1000  invested  in  a  manu- 
facturing plant  that  pays  8%  in  dividends  each  year? 

3.  Why  is  a  $100  share  of  stock  that  pays  $  12  in  divi- 
dends each  year  worth  more  than  $  100  ? 

4.  Why  is  a  $100  share  of  stock  that  pays  only  $2  in 
dividends  each  year  worth  less  than  $  100  ? 

5.  1|%  dividend  payable  quarterly  is  equivalent  to  what 
per  cent  payable  annually  ? 

6.  $  60  per  year  is  the  dividend  on  $  1200  worth  of  stock 
par  value.     Find  the  rate  of  dividend. 

7.  I  receive  $120  from  a  dividend  of  6%.  What  is  the 
par  value  of  my  stock  ? 

8.  Mr.  Johnston  owns  100  shares  of  stock  in  a  company 
whose  capital  is  $200000.  If  a  dividend  of  8%  is  declared, 
find  the  amount  of  the  check  that  will  pay  the  whole  divi- 
dend ;    the  amount  of  Mr.  Johnston's  share. 

Observe:    1.    Dividends  are  always   declared  on   the  par  valne  of  a 
stock. 

2.   Incomes  are  always  reckoned  on  how  much  a  stock  costs. 


330  STOCKS   AND   BONDS 

9.    A  dividend  of  6  %  is  declared  on  a  stock,  par  value  $100, 
purchased  at  $  120.      What  %  is  received  on  the  investment  ? 

6%  of  $  100  =  $  6,  income  on  one  share 

<|  120  =  cost  of  one  share 
$  6  h-$120  =  .05,or5% 

10.  A  share  of  stock,  par  value  $  100,  is  sold  at  $  250. 
What  is  the  per  cent  of  income  if  an  annual  dividend  of 
10%  is  declared? 

Find  the  rate  of  income  when  : 

11.  $150  is  paid  for  9%  stock,  par  value  1 100. 

12.  $133^  is  paid  for  6%  stock,  par  value  $100. 

13.  $75  is  paid  for  8%  stock,  par  value  $50. 

14.  $  80  is  paid  for  5%  stock,  par  value  $100. 

15.  $50  is  paid  for  4  %  stock,  par  value  $100. 

16.  Would  a  stock  yielding  6%  have  to  be  purchased  for 
more  or  less  than  par  value  to  yield  8%  on  the  investment  ? 
Explain  why. 

17.  Explain  why  a  stock,  par  value  $100,  dividend  12%, 
yields  only  6%  on  the  mone}'"  invested  when  purchased  at 
$200. 

18.  A  man  buys  120  shares  of  stock  at  137|,  and  receives 
a  6%  dividend.  He  sells  it  at  141f.  Find  his  net  profits 
on  the  investment  after  paying  brokerage  at  -|  %  each  for 
buying  and  selling. 

19.  Which  yields  the  better  income  and  how  much,  6% 
stock  at  $  120  or  4%  stock  at  $  85? 

20.  The  Amidon  Asbestos  Co.  is  capitalized  at  $80000. 
The  gross  receipts  for  a  year  are  $  170000.  The  expenses, 
material,  and  repairs  amount  to  $  14(3000.  If  $  14000  is  put 
in  the  surplus  fund,  what  dividend  can  be  declared  from  the 
balance  ? 


BONDS  331 

21.  A  gas  company  declares  a  dividend  of  8%  which 
amounts  to  $64000.     What  is  its  capitalization  ? 

22.  A  bank  is  capitalized  at  1100000,  and  pays  S% 
dividend.     How  much  is  the  dividend  on  3(3  shares? 

23.  How  much  must  be  invested  in  0%  stock,  at  108, 
brokerage  -|%,  to  yield  an  annual  income  of  I  366? 

Since     $1     of     stock 
8  366  -=-  $.06  =  6100;  $6100,  par  value     yields  $  .06  income,  the 

1.08^  x$  6100  =  $ 6595.63,  sum  invested     par  value  to  yield  §  366 

must  be  as  many  dollars 
as  $.06  is  contained  times  in  $366,  or  $6100.  Adding  brokerage,  the  sum 
invested  must  be  1.08$  times  $6100,  or  $6595.63. 

24.  If  a  stock  paying  3%%  semiannual  dividend  is  quoted 
at  120,  how  much  must  be  invested  in  it  to  produce  an 
annual  income  of  81400,  brokerage  \°fo  ? 

What  sum  must  be  invested,  at  \  %  brokerage,  in  : 

25.  3i%  stock,  at  104,  to  yield  an  annual  income  of  $245  ? 

26.  5%  stock,  at  109,  to  yield  an  annual  income  of  $1675  ? 

27.  4^%  stock,  at  116  J,  to  yield  an  annual  income  of 
$364.50^? 

BONDS 

When  corporations  need  large  sums  of  money  to  carry  on 
their  business,  instead  of  issuing  more  stock,  they  frequently 
issue  a  series  of  bonds  payable  at  some  future  date  with  in- 
terest. 

Bonds  are  written  obligations,  under  seal,  by  which  cor- 
porations or  governments  bind  themselves  to  pay  specified 
sums,  at  a  fixed  rate  of  interest,  at  or  before  the  time  speci- 
fied in  the  bonds. 

The  bonds  of  a  business  corporation  are  secured  by  a 
mortgage  on  its  property.     This    mortgage    authorizes    the 


332  STOCKS   AND   BONDS 

sale  of  the  property  in  case  the  conditions  of  the  bonds  are 
not  fulfilled.  The  bonds  of  governments  are  without 
mortgage. 

Bonds  and  stocks  are  at  a  premium  when  they  sell  for 
more  than  the  face,  or  par  value  ;  at  a  discount  when  they 
sell  for  less  than  the  face,  or  par  value. 

Coupon 


ACME  GL2ASS  COMPANY 

will    pay  to  Bearer  at  the 

Colonial  Erust  GTo.  of  $ tttsuttrg,  $a. 

on  the  first  day  of  June,  A.  D.,  1907, 

in  United  States  Gold  Coin,  being  six  months'  Interest 
on  Bond  No.  501 

fawve&  &hui&,  Treasurer. 


A  coupon  bond  is  a  bond  with  interest  coupons  attached. 
These  coupons  are  detached  when  the  interest  is  due,  and  the 
amount  may  be  collected  personally  or  through  a  bank. 
Coupon  bonds  are  payable  to  the  bearer. 

A  registered  bond  is  a  bond  registered  on  the  books  of 
the  corporation  issuing  it.  The  interest  when  due  is  sent 
by  check  to  the  owner.  Registered  bonds  are  payable  to  the 
owner  or  to  his  assignee. 

The  name  of  a  bond  often  indicates  its  rate  of  interest 
and  the  time  when  the  bond  is  due.  Thus,  "  U.  S.  4's,  1907," 
are  United  States  4  %  bonds,  due  in  1907  ;  "  Western  Union 
7's,    1920,"    are    Western    Union    bonds,  due  in  1920,  and 


BONDS  333 

bearing  ~<f0  interest;    "  TT.  S.  Steel  7's,"  are  United  States 
Steel  bonds,  bearing  7%  interest. 

Stock  or  bond  quotations  are  the  prices  at  which  stocks  and  bonds  are 
selling.  Thus,  B.  &  O.  t's  quoted  at  96  means  that  Baltimore  &  Ohio 
bonds  are  selling  at  96%  of  their  par  value  The  buyer  pays  96  4-  \ 
brokerage  =  96|,  or  $96,125,  per  share.  The  seller  receives  96  —  £  broker- 
age =  95|,  or  $95,875,  per  share. 

Comparative  Study 

Stockholders  are  the  otoners  of  corporate  property;  bondholders  are 
creditors  who  have  loaned  money  to  the  corporation  or  government. 
Bonds  bear  interest  at  a  fixed  rate  and  mature  at  a  time  specified  in  the 
bond,  stocks  continue  while  the  corporation  exists  and  pay  dividends 
according  to  the  earnings  of  the  company. 

Commission  or  brokerage  in  commission  is  reckoned  on  the  actual 
amount  of  goods  sold,  or  the  amount  of  money  involved  in  a  transaction  ; 
brokerage  in  stocks  and  bonds  is  always  reckoned  on  the  par  value  of  the 
stocks  or  bonds  bought  or  sold. 

Problems  in  Stocks  and  Bonds 

1.  Find  the  cost  of  15  $1000  United  States  bonds  at 
103|,  brokerage  \%. 

2.  How  many  Mound  City  water  bonds,  at  4|  %  premium, 
can  be  purchased  for  85225,  brokerage  not  included  ? 

3.  Find  the  par  value  of  4%  government  bonds  that 
yield  $1200  annually. 

4.  Find  the  face  of  a  3%  bond,  when  an  interest  coupon 
brings  $60  annually. 

5.  A  man  desires  to  invest  in  4%  bonds  sufficient  to  yield 
an  income  of  $1200  per  year.  If  the  bonds  are  selling  at  118, 
find  the  amount  that  must  be  invested,  including  brokerage. 

6.  A  $2000  4%  bond,  interest  payable  semiannually,  is 
sold  after  one  interest  period  at  10%  premium.  Find  the  per 
cent  of  gain  on  the  investment  if  the  bond  was  bought  at  par. 


334  STOCKS   AND   BONDS 

7.  $5  is  the  dividend  on  a  1100  stock  bought  at  180. 
Find  the  rate  of  income  on  the  investment. 

8.  Copper  stock,  par  value  $10  and  paying  24%  divi- 
dend, is  bought  at  $40.  No  allowance  being  made  for 
brokerage,  find  the  rate  of  income  from  the  investment. 

9.  I  purchase  100  shares  of  stock,  par  value  $50,  at  $65 
and,  after  receiving  2  dividends  of  2%  each,  sell  at  $78. 
Find  my  gain,  brokerage  -|  %  in  each  transaction. 

10.  Compute  the  rate  of  income  from  5%  stock  bought  at 
80  ;  at  90  ;   at  100  ;  at  120  ;   at  125. 

11.  My  income  from  G  %>  bonds  is  $240  per  year.  How 
much  have  I  invested  ? 

12.  I  bought  24  shares  of  mining  'stock  at  89  and,  after 
keeping  it  3  years,  sold  it  at  39.  As  no  dividends  were  paid, 
find  my  loss,  money  being  worth  6%  simple  interest. 

13.  A  $1000  5%  bond,  bought  at  par,  after  paying  6  annual 
dividends,  is  sold  for  $.60  on  the  dollar.  Find  the  loss, 
money  being  worth  5%  simple  interest. 

14.  A  certain  stock  bought  in  1904  at  40^  per  share 
was  sold  in  1906  at  $2.40  per  share.  Find  the  gain  per 
cent  on  the  investment. 

15.  A  $1000  5%  bond  due  in  10  years  was  purchased  for 
81100.  Find  the  average  rate  of  interest  on  the  investment, 
if  the  bond  is  held  to  maturity. 

The  total  income  on  the  bond  for  10  years  at  5%  =  $500.  Loss  by 
redemption  of  bond  §1100  -  81000  =  $100.  Total  income  in  10  yr.  = 
$500  -  $100  =  $400.  Average  annual  income  =  ^  of  $400  =  $40. 
Average  annual  rate  =  $40  -*-  $1100  =  3^%. 

16.  A  §2000  4  %  bond  due  in  5  yr.  was  bought  for  $1900. 
Find  average  rate  of  interest,  if  bond  is  held  to  maturity. 

Note.     The  purchaser  gains  $100  when  the  bond  is  redeemed. 


TEST   PROBLEMS   IN   PERCENTAGE 

1.  Mr.  Byers's  farm  is  valued  at  $18000.  He  pays  4-^j 
mills  taxes  on  an  80%  valuation  of  it.     Find  his  tax. 

2.  An  agent  buys  30  tons  of  fertilizer,  at  $1.50  per  hun- 
dred, 20%,  10%  off.  Terms:  30  days  net,  or  2%  for  cash. 
If  he  pays  cash,  find  the  cost. 

3.  A  western  farmer  sells  10000  bu.  of  wheat,  \t  per 
bushel  brokerage,  at  89^.  After  deducting  freight  and 
drayage  of  $>67A,  find  the  net  amount  of  the  sale. 

4.  An  Iowa  farmer  buys  cattle  for  $1500,  and  sells  them 
for  $2350.  If  the  grazing  and  feeding  are  20%  of  the  cost, 
find  the  per  cent  of  profit  on  the  sale. 

5.  A  merchant  has  a  note  against  Mr.  Johnston  for  $500, 
bearing  6  %  interest,  dated  June  1,  1906,  due  in  one  year. 
If  he  discounts  the  note  at  his  bank  March  1,  1907,  at  7  %, 
find  the  proceeds. 

6.  A  farmer  has  the  following  annual  insurance  on  his  prop- 
erty :  house  valued  at  $  2000,  insured  at  |  % ;  barn  valued  at 
?2500,  insured  at  T9o%;  grain  valued  at  $1000,  insured  at 
|%;  live  stock  $1200,  insured  at  |%.  If  twice  the  annual 
premium  covers  the  cost  of  the  insurance  for  3  years,  find 
the  yearly  cost  if  his  property  was  insured  for  3  years. 

7.  Mr.   Ames,  who  keeps  a  general  store,  sold  goods  in 

one  year  amounting  to  $24000.     If   he  has  an  average  of 

20%  profit  on  the  cost  of  the  goods,  find  his  profits  for  the 

year. 

335 


336       TEST  PROBLEMS  IN  PERCENTAGE 

8.  A  manufacturer,  owing  to  a  depression  in  business, 
offers  goods  at  12|%  discount,  but  finally  sells  at  a  further 
discount  of  8%.     Find  the  entire  per  cent  of  discount. 

9.  What  per  cent  is  gained  by  buying  stocks  at  15  °}0 
discount  and  selling  at  5  %  premium,  brokerage  \  °J0  ? 

10.  The  tax  rate  in  a  certain  city  is  17  mills  on  the  dollar 
on  a  valuation  of  $66390.  Find  the  tax  on  a  property  val- 
ued at  $12500. 

11.  A  salesman  who  received  a  salary  of  $2400  and  $1500 
expenses,  sold  $75000  worth  of  goods.  In  addition  he  re- 
ceived 2%  on  all  sales  over  $60000.  What  per  cent  of  the 
selling  price  of  the  goods  did  it  cost  the  firm  to  sell  them  ? 

12.  A  man  buys  through  his  broker  10  shares  of  railroad 
stock  (par  value  $100)  at  $125  per  share.  After  receiving 
5  semiannual  dividends  of  3%  each,  he  sells  the  stock  at 
$131^.     Find  the  rate  per  cent  of  gain  on  the  investment. 

13.  By  selling  a  piano  at  40  %  above  cost,  a  profit  of  $150 
is  realized.  For  how  much  must  the  piano  be  sold  to  realize 
a  profit  of  56  (f0  ? 

14.  A  collector  is  given  a  bill  of  $1500  to  collect  at  5%. 
He  succeeds  in  collecting  90  cents  on  the  dollar.  Find  how 
much  is  due  his  client  and  how  much  is  the  collector's  com- 
mission. 

15.  A  house  and  lot  cost  $6000.  The  insurance  averages 
$14,  taxes  $50,  and  repairs  $56  annually.  For  how  much 
must  the  house  rent  per  year  to  realize  6%  net  on  the 
investment  ? 

16.  A  house  rents  for  $40  per  month,  and  it  costs  the 
owner  on  an  average  $125  per  year  for  insurance,  taxes, 
and  repairs.  If  the  property  yields  him  5%  net  on  the 
investment,  find  the  cost  of  the  house. 


RATIO   AND   PROPORTION 

RATIO 

1.  The  quotient  of  30  -f-  10  is  3.  Compare  30  with  3  in 
such  a  way  as  to  show  how  many  times  3  is  contained  in  30. 
What,  then,  is  the  relation  of  30  to  3? 

Ratio  is  the  relation  of  two  similar  numbers  as  expressed 
by  the  quotient  of  the  first  divided  by  the  second. 

2.  What  is  the  ratio  of  10  to  8  ?  of  12  to  4  ?  of  3  to  6?  of 
2  yd.  to  8  yd.?  of  $12  to  83. 

Since  the  division  of  two  similar  numbers  gives  an  abstract 
quotient,  all  ratios  are  abstract. 

The  sign  of  ratio  is  a  colon  :  placed  between  the  numbers. 
Thus,  the  ratio  of  12  to  3  is  written  12  :  3.  It  is  read,  l»  the 
ratio  of  12  to  3."     It  may  be  written  also  12  ~-  3,  or  J^-. 

The  terms  of  a  ratio  are  the  numbers  compared.     The  first 
is  the  antecedent ;  the  second  the  consequent. 
19  #  r   _  antecedent  _  19  _i_r  --  dividend      !-      numerator 


consequent  divisor         0       denominator 

Since  the  antecedent  of  a  ratio  may  be  regarded  as  the 
numerator,  and  the  consequent  as  the  denominator  of  a  frac- 
tion, both  terms  of  a  ratio  may  be  multiplied  or  divided  by  the 
same  number  without  changing  the  value  of  the  ratio. 

Find  the  ratio  of  : 


3. 

10  to  5 

7.    18  to  9 

11. 

40  to  10 

15. 

50  to  25 

4. 

5  to  15 

8.    27  to  9 

12. 

8  to  24 

16. 

24  to  8 

5. 

8  to  2 

9.    35  to  5 

13. 

2  to] 

17. 

4  to  1 

6. 

2  t0  i" 

HAM.   COHP1 

10.      J  to  1 

..    AKITH.  —  22 

14. 

:;37 

fto| 

18. 

ftoj 

338  RATIO    AND   PROPORTION 

Written  Work 
Find  the  value  of  the  following  ratios  : 


1. 

125  :  25 

5. 

-2-     to  -1- 
3      lo  12 

9. 

$225  to  $2.25 

2. 

6.25  :  25 

6. 

(3.4    to  16 

10. 

3  yd.  to  3  ft. 

3. 

1     toj 

7. 

37|  to  200 

11. 

75%  tol2|% 

4. 

i     toH 

8. 

&2}  to  500 

12. 

1  mi.  to  1  rd. 

SIMPLE   PROPORTION 

Proportion  is  an  equality  of  ratios;  thus,  12:  6  =  8:  4  or 
-g2-  =  |  is  a  proportion. 

Proportion  is  generally  indicated  by  the  equality  sign  or 
by  a  double  colon  :  :  between  the  ratios.  Thus,  12:6  as 
8  :  4,  is  written,  12  :  6  =  8  :  4,  or  12  :  6  :  :  8  :  4. 

A  proportion  may  be  read  in  two  ways  ;  thus,  12:6  =  8:4 
is  read,  "  The  ratio  of  12  to  6  is  equal  to  the  ratio  of  8  to  4," 
or,  "12  is  to  6  as  8  is  to  4." 

The  extremes  are  the  first  and  the  fourth  terms  of  a  pro- 
portion ;  the  means  are  the  second  and  the  third  terms. 

In  15 :  5  =  12  : 4,  the  extremes  are  15  and  4 ;  the  means,  5  and  12. 

Find  the  product  of  the  means ;  then  the  product  of  the 
extremes  : 

1.  8  :  4  =  10  :  5  3.    24  :  4  =  36  :  6  5.    §  =  f 

2.  15:3  =  30:6  4.  |  =  T%  6.    |  =  ^ 

Observe  how  the  product  of  the  extremes  in  each  proportion 
compares  with  the  product  of  the  means. 

In  every  proportion  the  product  of  the  means  is  equal  to  the 
product  of  the  extremes. 


SIMPLE   PROPORTION 


:;:',!) 


Written  Work 
Find  the  value  of  x,  the  unknown  term : 

1.  36:    0=24:    x 

Then,  30  times  x,  or  36  x  =  144,  and  once  x,  or  x  =  4. 

2.  15  :  25  =    x  :  40 

Then,  25  x  =  15  x  40,  or  600,  and  x  =  24. 

8. 

9. 
10. 
11. 
12. 


3. 

60  :  15  =  75  :  x 

4. 

75:  a;  =90:  18 

5. 

40:  z=72:18 

6. 

x.:  30  =  8  :  48 

7. 

a:  45  =  7  :  63 

3 

5 

5 
8 

2  _  q 

3  —  ' 

z=  25 

<  .5 

:  1.5=2.5 

6.25 

:  2.5=  x 

60 

150=  36 

X 

8 
x 
1 
a; 


13.  If  8  sheep  cost  $48,  how  much  will  20  sheep  cost  ? 

8  sheep  cost  $48 
20  sheep  cost  $  x 

Since  ratio  is  the  relation  of  two  similar  numbers,  8  sheep  and  20 
sheep  form  one  ratio,  and  $48  and  $x,  the  other  ratio. 

Write  as  the  second  ratio  $48  :  $x.  Since  20  sheep  cost  more  than 
8  sheep,  $x  represents  a  larger  sum  than  $48.  Therefore,  as  the  larger 
number  is  the  consequent  of  the  second  ratio,  the  larger  number  must  be 
made  the  consequent  of  the  first  ratio.     The  proportion,  therefore,  is, 

8  sheep  :  20  sheep  =  $48  :  $z 
8x  =  $960 
x  =  $120 

14.  It  is  estimated  that  25  men  can  build  a  bridge  in  18 
days.  How  long  at  the  same  rate  will  it  take  15  men  to 
build  it  ? 

15.  How  much  will  30  bushels  of  potatoes  cost,  if  70 
bushels  cost  $42  ? 

16.  It  is  estimated  that  90  men  are  necessary  to  grade 
a  certain  street  in  45  days.  If  only  81  men  are  hired  to  do 
the  work,  how  long  will  it  take  them? 


340  RATIO  AND  PROPORTION 

17.  The  ratio  is  }.  The  first  term  is  |  of  (6x4).  What 
is  the  second  terra  ? 

18.  A  bankrupt's  debts  are  $32000,  and  his  assets  $10000. 
Counting  nothing  for  court  costs,  how  much  will  be  paid  on 
a  claim  of  $6150? 

19.  If  $2.25  is  paid  to  clean  35|-  square  yards  of  paper,  how 
much  at  the  same  rate  will  it  cost  to  clean  65|  square  yards  ? 

20.  A  bakery  sells  5^  loaves  weighing  6  oz.  when  flour  is 
$4.  What  size  loaves  should  they  sell  at  5^  when  flour  is 
$6  per  barrel? 

21.  A  map  is  drawn  on  a  scale  of  100  miles  to  |  of  an  inch. 
What  distance  is  represented  on  the  map  by  T5g  of  an  inch  ? 

22.  If  the  interest  on  $500  for  6  months  is  $15,  how 
much  is  the  interest  on  the  same  sum  for  1  year  4  months  ? 

23.  If  6.5  tons  of  coal  cost  $55.90,  how  much  will  9.25 
tons  cost  at  the  same  rate  ? 

24.  A  estimates  that  he  can  do  a  piece  of  work  in  20  days, 
working  8  hours  per  day.  How  long  will  it  take  him  to  do 
\  of  it,  working  10  hours  per  day  ? 

25.  Sound  travels  1120  feet  per  second.  How  long  will 
it  take  the  sound  of  a  cannon  to  travel  8  miles  ? 

26.  In  a  stamp  canceling  machine  1000  letters  were  can- 
celed in  one  minute  and  20  seconds.  If  the  machine  was  in 
operation  for  5  minutes  and  10  seconds,  how  many  letters  at 
the  same  rate  were  canceled  ? 

27.  A  monument  casts  a  shadow  150  feet  long.  At  the 
same  time  a  post  3  feet  in  height  casts  a  shadow  2  feet  and 
6  inches  long.     Find  the  height  of  the  monument. 

28.  A  machine  for  making  pressed  brick  turns  out  7500 
brick  in  6  days.  How  large  an  order  for  pressed  brick  can 
be  filled  in  25  days  ?  * 


PARTITIVE  PROPORTION   AND   PARTNERSHIP       ^41 

29.  An  automobile  passed  5  mile-posts  in  8  minutes  10 
seconds.      How  many  miles  per  hour  was  it  moving? 

30.  It  is  estimated  that  24  men  working  18  days  can  re- 
pair a  certain  street.  The  contract  calls  for  the  work  to  be 
completed  in  8  days.   How  many  extra  men  must  be  employed? 

31.  It  is  estimated  that  GO  men  can  dig  a  sewer  on  Main 
Street  in  24  days.  The  contract  time  is  40  days.  How 
many  men  may  be  discharged  and  yet  have  the  work  com- 
pleted within  the  contract  time  ? 

32.  A's  property  is  assessed  at  $2750,  on  which  $37.90 
taxes  are  paid  each  year.  How  much  tax  should  B  pay  on 
his  property  assessed  at  $4375  ? 

33.  A  train  of  30  cars  of  ore  contains  1200  tons.  How 
many  cars  must  be  added  so  that  the  train  may  carry  2700 
tons  ? 

34.  A  city's  assessed  valuation  is  $5675000.  There  must 
be  raised  in  taxes  on  this  valuation  $  85125.  How  much  is 
Mr.  Templetons  tax  on  a  property  assessed  at  $15750? 

PARTITIVE  PROPORTION  AND  PARTNERSHIP 

Partitive  proportion  is  the  process  of  separating  a  number 
into  parts  proportional  to  two  or  more  numbers. 

Written  Work 
l.    Separate  180  into  parts  proportional  to  1,  2,  and  3. 

Since  the  parts  are  in  the  ratio  of  1,  2,  and  :5,  then  1  +  2  +  3,  or  G 

parts  =  180. 

The  1st  number  =  180  -    6,  or  30 
The  2d  number  =      2  x  30,  or  GO 
The  3d  number  =      3  x  30.  or  90 
Test :  30  +  60  +  90  =  180 ;  30  :  60  :  90=  1 :2: 3. 


342  RATIO   AND   PROPORTION 

2.  A  man  and  two  boys  earn  $162  and  agree  to  divide  it 
as  follows :  3  parts  to  the  man,  2  parts  to  the  first  boy,  and 
1  part  to  the  second  boy.     How  much  should  each  receive? 

3.  The  receipts  of  a  street  railway  in  one  month  are 
$15600,  and  the  expenses  are  to  the  profits  as  1  to  2.  Find 
the  expenses  and  the  net  savings. 

4.  Four  men  own  a  gold  mine  valued  at  $805000.  The 
parts  owned  by  each  are  in  the  ratio  of  6,  |,  f,  and  T9g.  Find 
each  man's  share  of  the  mine. 

5.  The  cost  of  shipping  a  train  load  of  2000  tons  of  iron 
ore  from  Duluth,  Minn.,  to  Bessemer,  Pa.,  is  $2800.  If  the 
lake  freight  is  to  the  railroad  freight  as  50  to  90,  find  each 
one's  share  of  the  freight  charges. 

6.  Two  railroads,  valued  at  $6900000  and  $23000000, 
share  charges  of  $299000  for  freight  carried  over  both 
roads  in  proportion  to  the  valuation  of  each  road.  Find  the 
earnings  apportioned  to  each  road. 

Partnership  is  the  associating  of  two  or  more  persons 
who  agree  to  combine  their  money,  labor,  goods,  skill,  or 
"  good  will "  in  some  enterprise,  and  to  share  the  profits  or 
losses  of  the  business  in  proportion  to  the  interest  each  part- 
ner owns. 

The  partnership  is  frequently  called  a  firm,  or  a  house,  and  derives 
its  name  from  the  persons  that  compose  it;  as,"  Brown  &  Hamilton." 

The  capital  of  a  partnership  is  the  sum  of  the  investments 
of  the  partners.  This  capital  may  be  money  or  anything  that 
has  a  money  value,  as  skill,  good  will,  experience,  labor,  etc. 

Gains  and  losses  in  a  common  partnership  are  usually  appor- 
tioned in  proportion  to  the  amount  of  capital  each  partner  invests 
and  the  length  of  time  such  capital  is  invested  ;  but  in  case  any 
partner  cannot  pay  his  proportionate  share  of  the  loss,  the  re- 
maining partners  are  liable  for  the  whole  loss. 


PARTITIVE   PROPORTION    AND   PARTNERSHIP      343 

Written  Work 

l.    A  and  B  engage  in  business ;   A  furnishes  $800  and  B, 
81200;  they  gain  $500.      What  is  each  man's  share? 

$800  +  $1200  =  $2000,  entire  capital 


SS,H) 

$2000 


=  I,  A's  share  of  the  capital 


®UQ0  =  §,  B's  share  of  the  capital 

$2000 

|  of  $500         =  8200.  A's  .share  of  the  gain 
|  of  $500         =  $300,  B's  share  of  the  gain 
Or,  $2000  :    $800  =  $500  :  $200 
$2000  :  $1200  =  $500  :  $300 

The  ratio  of  the  whole  capital  to  each  partner's  investment  is  equal  to 
the  ratio  of  whole  gain  or  loss  to  each  partner's  share  of  the  gain  or  loss. 

2.  A,  B,  and  C  engaged  in  manufacturing  iron.  A  in- 
vested 842000,  B  $96000,  and  C  his  skill,  valued  at  $72000. 
Their  profits  the  first  year  were  $12600.  How  much  was 
each  man's  gain  ? 

3.  M,  N,  and  R  formed  a  partnership;  M  furnished  |  of 
the  capital,  N  §,  and  R  the  remainder.  They  gained  $7560. 
What  was  each  man's  share  of  the  gain  ? 

4.  E,  F,  and  G  engaged  in  merchandizing  with  a  capital 
stock  of  $28000.  E  furnished  87000,  F  $6000,  and  G  the 
remainder.  They  gained  14f%  on  the  investment.  What 
was  each  man's  share  of  the  gain? 

5.  The  assets  of  a  firm  that  failed  in  business  were 
$3750  ;  their  liabilities  8  22000.  How  much  will  two  credit- 
ors, to  whom  they  owe  $7800  and  $5400  respectively,  receive? 

6.  A  storeroom  belonging  to  Smith,  Jones,  &  Brown 
was  entirely  destroyed  by  fire.  They  received  $9675  insur- 
ance. What  was  each  man's  share,  if  Smith  owned  ^,  Jones  ^, 
and  Brown  the  remainder  of  the  stock? 


344  RATIO   AND  PROPORTION 

7.  A  and  B  formed  a  partnership  January  1,  and  each 
invested  12500;  May  1  A  added  $500,  and  B  withdrew 
$500.  At  the  end  of  a  year  their  gain  was  $1800.  How 
much  should  each  one  receive? 

A's  capital,  $2500  for  4  mo.  =  $10000  for  1  mo. 
A's  capital,  $3000  for  8  mo.  =  $24000  for  1  mo. 


A's  total  capital 

=  $34000  for  1  mo. 

B's  capital,  $2500  for  4 

mo. 

=  $10000  for  1  mo. 

B's  capital,  $2000  for  8 

mo. 

=  $16000  for  1  mo. 

B's  total  capital 

=  $26000  for  1  mo. 

Total  capital  of  both 

=  $60000  for  1  mo. 

A ,        •         34000 
As  Gram  = ,  or 

fe            60000 

?0> 

of  $1800  =  $1020. 

-o,        ■         26000 

B  s  sain  = ,  oi 

&             60000 

1  3 
3T>> 

of  $1800  =  $780. 

$1020  -f  $780  =  $1800,  total  gain. 

Test: 

8.  M  and  N  formed  a  partnership  for  2  years.  M  put 
in  $6400;  N  put  in  $3600  and  at  the  end  of  6  months 
added  $1400.  Their  settlement  at  the  end  of  2  years 
showed  $7956  profits.     How  should  it  be  divided? 

9.  R  and  S  began  business  as  partners  April  1,  1904, 
each  investing  $5000.  On  July  1,  1904,  R  added  $3000 
and  S,  $2000.  They  dissolved  partnership  January  1,  1905, 
sharing  a  profit  of  $3150.     Find  each  one's  share. 

10.  A,  B,  and  C  formed  a  partnership  for  3  years.  A  put 
in  $10000,  B  $8000,  and  C  $6000.  A  withdrew  $2000  at 
the  end  of  18  months.  They  dissolved  partnership  at  the 
end  of  2  years  with  a  loss  of  $4750.  As  nothing  could  be 
collected  from  C,  what  proportionate  share  of  the  loss  should 
A  and  B  pay? 


PROBLEMS   FOR   ORAL   AND   WRITTEN 

ANALYSIS 

1.  Two  properties  are  valued  at  $1000;  J  of  the  value 
of  the  first  equals  f  of  the  value  of  the  second.  Find  the 
value  of  each. 

2.  At  a  certain  election  1080  votes  were  cast  for  A  and  B  ; 
|  of  the  votes  cast  for  A  equaled  f  of  those  cast  for  B.  How 
many  votes  were  cast  for  each  candidate  ? 

Solution.  —  f  of  A's  vote  =  |  of  B's  vote. 

\  of  A's  vote  =  i  of  %  of  B's  vote,  or  1  of  B's  vote. 
|  or  A's  vote  =  4  x  4,  of  B's  vote,  or  4.  of  B's  vote. 

|  of  B's  vote  =  B's  vote, 
f  of  B's  vote  =  A's  vote. 


|  of  B's  vote  =  vote  of  both,  or  1080  votes. 
B's  vote  =  600. 
A's  vote  =  480. 

3.  A  real  estate  dealer  paid  87200  for  two  city  lots;  f  of 
the  cost  of  the  first  lot  equaled  ^  of  the  cost  of  the  second. 
How  much  did  each  cost? 

4.  A  mill  and  machinery  cost  $27000;  f  of  the  cost  of 
the  mill  equaled  f  of  the  cost  of  the  machinery.  How 
much  did  the  machinery  cost? 

5.  What  per  cent  of  a  day  are  12  hours?  6  hours?  36 
hours? 

6.  |  of  Frank's  money  equals  £  of  Henry's,  and  Frank  has 
83  more  than  Henry.     How  much  has  each? 

345 


346    PROBLEMS   FOR  ORAL   AND   WRITTEN   ANALYSIS 

7.  Walter  and  Philip  bought  sleds;  f  of  the  cost  of 
Walter's  sled  equaled  |  of  the  cost  of  Philip's;  both  sleds 
cost  $2.70.     How  much  did  each  cost? 

8.  A  pair  of  shoes  that  cost  a  dealer  $2.50  were  sold  for 
$3.50.     What  was  his  gain  per  cent? 

9.  An  estate  was  so  divided  between  two  sons  that  the 
share  of  the  elder  was  to  that  of  the  younger  as  |  to  ^.  If 
the  elder  son  received  $1000  more  than  the  younger,  what 
was  the  value  of  the  estate  ? 

10.  Brown  and  Long  were  partners  in  business  ;  Brown 
furnished  |  as  much  capital  as  Long,  and  their  profits  for* 
the  first  year  were  $2250,  which  was  divided  in  the  ratio  of 
the  capital  invested.     What  was  the  share  of  each  ? 

11.  In  a  partnership  A  invested  |  as  much  as  B,  and  C  in- 
vested |  as  much  as  B  ;  they  shared  a  loss  of  $  2000.  How 
much  should  C  pay  ? 

12.  A  piano  sold  for  $360,  which  was  at  a  loss  of  20  %. 
What  was  the  cost? 

13.  Moore,  Silvens,  and  Rogers  were  partners  in  business 
and  made  a  profit  of  $  4500.  Moore  owned  y4^  of  the  stock, 
Silvens  •§,  and  Rogers  ^.  What  was  each  partner's  share  of 
the  total  profit  ? 

14.  A  clerk's  expenses  are  $30  a  month,  which  is  66|  % 
of  his  salary.     How  much  is  his  salary  ? 

15.  A  stone  cutter  received  $4  a  day  for  his  labor  and 
paid  $6  a  week  for  his  board.  At  the  end  of  16  weeks  he 
had  saved  $212.      How  many  days  did  he  work  ? 

16.  If  in  an  investment  |  of  A's  capital  equaled  |  of  B's, 
and  A  received  $900  for  managing  the  business,  how  should 
profits  of  $5100,  including  cost  of  management,  be  divided? 


PROBLEMS    FOR   ORAL   AND    WRITTEN    ANALYSIS     347 

17.  A  wagon  was  sold  for  I  12,  which  was  12.]  %  less  than 
the  price  paid.     What  was  the  cost  of  the  wagon? 

18.  A  carpenter's  wages  were  $3.50  a  day,  and  he  paid 
50  cents  a  day  for  his  board.  If  in  40  days  he  saved  $>99, 
how  many  days  was  he  idle  ? 

19.  A  real  estate  dealer  bought  some  lots  at  #150  each, 
and  twice  as  many  at  8175  each.  He  sold  them  at  $200 
each,  thereby  gaining  $800.     How  many  did  he  buy  in  all? 

20.  A  manufacturer  pays  boys  $1,  women  $1.25,  and  men 
$1.75  a  day,  and  his  weekly  pay  roll  is  $348.  He  employs 
three  times  as  many  boys  as  men,  and  twice  as  many  women 
as  men.     How  many  persons  does  he  employ  ? 

21.  A  farmer  paid  $7200  for  two  farms  of  equal  size,  pay- 
ing $50  an  acre  for  one  and  $40  an  acre  for  another.  How 
many  acres  were  there  in  both  farms  ? 

22.  A  dealer  bought  20  dozen  glasses  at  50^  per  dozen. 
At  what  price  per  dozen  must  he  sell  them  to  make  a  profit 
of  20  %  on  the  transaction  ? 

23.  It  is  estimated  that  80  men  can  make  an  excavation 
for  a  public  building  in  30  days.  After  working  12  days, 
\  of  the  men  were  discharged.  In  how  many  days  could  the 
remainder  finish  the  work  ? 

24.  A  father  desires  that  the  amount  of  $5000  for  6  years 
at  0  °J0  shall  be  divided  between  his  son  and  daughter  in  the 
ratio  of  8  to  9.     Find  the  share  of  each. 

25.  An  architect  gets  a  commission  of  5%  for  drawing 
plans  and  superintending  the  construction  of  a  building  cost- 
ing 825000.     How  much  is  his  commission  ? 

26.  The  interest  on  |  of  Robert's  money  and  |  of  Samuel's 
money  for  4|  years,  at  6%,  is  $81  and  $121.50  respectively. 
How  much  money  has  each? 


348     PROBLEMS   FOR   ORAL   AND   WRITTEN   ANALYSIS 

- 

27.  The  sum  of  E's  and  F's  money  being  on  interest  for 
five  years,  at  5%,  amounts  to  $3000.  How  much  money  has 
each,  if  E's  is  f  of  F's? 

28.  The  amount  of  a  certain  principal  for  4  years  at  a 
certain  per  cent  is  $620  ;  and  for  7  years,  $710.  Find  the 
principal  and  the  rate  per  cent. 

29.  30  is  6  %  of  what  number?  25  is  |  %  of  what  number? 

30.  It  is  estimated  that  15  men  can  build  an  embankment 
of  earth  in  20  days.  If  5  additional  men  are  employed,  in 
how  many  days  can  it  be  built? 

31.  Harley  spent  ^  of  his  money  and  $5  more  for  a  suit  of 
clothes,  and  had  $11  remaining.  How  much  money  had  he 
at  first? 

32.  After  paying  25  %  of  his  debts,  a  merchant  found  that 
$240  would  pay  the  remainder.  How  much  did  he  owe  at 
first? 

33.  How  shall  I  mark  goods  that  cost  $750,  so  that  I  can 
deduct  10  °J0  from  the  marked  price,  and  yet  make  20  %  on 
the  cost? 

34.  A  speculator  bought  wheat  at  80^  per  bushel  and  sold 
it  at  90^  per  bushel.  How  many  bushels  did  he  buy  if  his 
gain  was  $2000? 

35.  An  agent  remitted  $95  as  the  proceeds  of  an  account 
he  collected.  How  much  did  he  retain  if  his  rate  of  commis- 
sion was  5  %  ? 

36.  A  bankrupt,  who  owed  $12000,  paid  60^  on  the  dol- 
lar.    Find  A's  claim,  and  his  loss  if  he  received  $600. 

37.  8  men  take  equal  shares  in  an  oil  lease,  agreeing  to 
give  the  owner  of  the  land  \  royalty  on  all  oil  produced. 
How  much  greater  interest  in  the  oil  has  the  owner  than  any 
of  the  other  men  ? 


LONGITUDE   AND   TIME 


Meridians  are  im- 
aginary lines  passing 
north  and  south  from 
one  pole  of  the  earth 
to  the  other. 

The  equator  is  an 
imaginary  line  pass- 
ing around  the  earth 
midway  between  the 
poles. 

These  imaginary  lines 
aid  in  locating  places  on 
the  earth  and  in  determin- 
ing differences  in  time. 

Observe  that  the  equator  is   a  circumference  of  a  circle ;  therefore 
distances  along  it  are  measured  in  degrees. 

The  prime  meridian   is  a  meridian  from  which  time  and 
place,  east  and  west,  are  reckoned. 

The  meridian  passing  through  the  Royal  Observatory  at  Greenwich, 
England,  is  the  prime  meridian  in  common  use. 

Longitude  is  the  distance  east  or  west  of  this  prime  merid- 
ian measured  in  degrees. 

Places  east  of  this  prime  meridian  have  east  longitude;  places  west  of 
this  prime  meridian  have  ivest  longitude. 

From  the  time  the  sun's  rays  are  vertical  over  any  meridian 
until  they  are  vertical  again  it  is  24  hours.     Therefore,  any 

349 


350  LONGITUDE   AND   TIME 

point  passes  through  360°  in  one  rotation  of  the  earth  on  its 
axis. 

Since  360°  of  longitude  pass  under  the  sun's  vertical  rays 
during  24  hours,  how  many  degrees  pass  during  12  hours  ? 
1  hour  ? 

Since  ■£%  of  360°  or  15°  pass  under  the  sun's  rays  in  1  hour, 
then  1  hour  of  time  corresponds  to  15°  of  longitude. 

Since  15°  of  longitude  correspond  to  1  hour  of  time,  ^  of 
15°  or  |°,  or  15'  of  longitude,  correspond  to  1  minute  of  time, 
and  15"  of  longitude  to  1  second  of  time. 

Table  of  relation  between  longitude  and  time  : 


360°  of  longitude  correspond  to  24  hours  of  time 
15°  of  longitude  correspond    to    1  hour  of  time 
15'  of  longitude  correspond   to    1  minute  of  time 
15"  of  longitude  correspond  to     1  second  of  time 
1°  of  longitude  corresponds  to    4  minutes  of  time 
1'  of  longitude  corresponds  to    4  seconds  of  time 


When  the  sun's  rays  are  vertical  on  the  90th  meridian, 
all  places  on  that  meridian  have  noon. 

The  rotation  of  the  earth  from  west  to  east  makes  the  sun 
appear  to  move  from  east  to  west.  The  Mercator's  map  on 
p.  351  shows  that  when  it  is  noon  at  Greenwich,  it  is  before 
noon  or  earlier  at  all  places  west,  because  the  sun's  rays  are 
not  yet  vertical  on  any  meridian  west  of  the  prime  meridian. 
It  is  after  noon  or  later  at  all  places  east,  because  the  sun's 
rays  have  already  been  vertical  on  all  meridians  east  of  the 
prime  meridian. 

Examine  the  map.  What  time  is  it  on  the  meridian  of 
Greenwich  ?  45°  east  of  Greenwich  ?  45°  west  of  Greenwich  ? 
In  traveling  from  London  to  New  York  would  a  watch  be 
set  forward  or  backward'?  about  how  much?  About  how 
much  change  in  time  must  be  made  in  traveling  from  Cal- 


LONGITUDE   AND   TIME 


351 


cutta    westward    to    Sun    Francisco?    from    Honolulu    east- 
ward to  Cape  Town  ? 


135        105        75 


45  15  15 


45  75 


105        135 


East    160         150         I20i°"9  90  w«>  60 


30 


30  60  Long  90  East  120 


Map  showing  Noon,  February  1,  at  Greenwich 

What  is  the  difference  in  degrees  between  a  place  30°  east 
longitude  and  a  place  45°  east  longitude?  What  is  the 
difference  in  time  and  which  has  the  earlier  time  ? 


Table  of  Longitude  of  Some  Important  Places 


London 

0°     5'  48"  W. 

Cape  Town 

18°  28'  45"  E. 

New  York 

74°    0'     3"  W. 

Honolulu 

157°  50'  30"  W. 

Pittsburg 

80°     2'     0"  \V. 

Tokyo 

139°   11'  30"  E. 

Washington 

77°     3'  00"  W. 

Manila 

120°  58'     0"  E. 

Chicago 

87°  30'  42"  W. 

Canton 

113°  10'  30"  E. 

San  Francisco 

122°  2.">'  42"  W. 

Berlin 

13°  23'  44"  E. 

Boston 

71°     3'  50"  \V. 

Rome 

12°  27'   11"  E. 

1  >>•  iiver 

104°  58'     ()"  W. 

Paiis 

2°  20'  15"  E. 

Longitudes  are  given  to  the  nearest  seconds. 


352 


LONGITUDE   AND   TIME 


Written  Work 

1.  When  it  is  noon,  solar  time,  at  Paris,  what  is  the  solar 
time  at  New  York  ? 

Since  the  earth  rotates  15°  in  1  hr.,  15' 
in  1  tnin.,  and  15"  in  1  sec,  the  differ- 
ence in  time  is  as  many  hours,  minutes, 
and  seconds  as  there  are  degrees,  minutes, 
and  seconds  in  Tx5  of  the  difference  in 
longitude. 

The  difference  in  time  is  5  hours,  5  minutes,  21|  seconds.  Since  New 
York  is  west  of  Paris,  the  time  in  New  York  is  earlier ;  that  is,  when  it  is 
noon  at  Paris,  't  is  6  o'clock,  54  min.,  and  38|  sec.  a.m.  at  New  York. 


2° 

20' 

15"  E. 

74° 

0' 

03"  W. 

15)76° 

20' 

18" 

5° 

5' 

91  \U 
*dl5 

5  hr.  5 

min. 

21isec. 

5rir-.5niin.  2iys     .|  12 Noon 


NewYork       'n  lon3J6°20'\&  Paris 


What  is  the  difference  in  longitude  between  the  two  places?  the  dif- 
ference in  time?  In  going  west  from  Paris  to  New  York  would  a  trav- 
eler set  his  watch  forward  or  backward?  how  much? 

Note.  —  Study  this  diagram  and  make  a  similar  one  for  each  problem. 

Find  difference  in  degrees,  difference  in  time,  and  which 
place  has  earlier  time  : 

Places 

2.  60°  W.  and  45°  W. 

3.  120°  W.  and  75°  W. 

4.  15°  W.  and  45°  E. 

5.  30°    E.  and  60°  E. 

6.  75°  W.  and  30°  E. 


Places 

7. 

120°  W.  and  30°  E. 

8. 

90°  W.  and  30°  E. 

9. 

135°    E.  and  30°  E. 

10. 

45°  W.  and  60°  E. 

11. 

45°    E.  and  15°  E. 

LONGITUDE  AND  TIME  353 

When  the  sun's  rays  are  vertical  on  the  meridian  of  Wash- 
ington, find  the  solar  time  in  the  following  places  : 

12.  Denver  15.    Paris  18.    Berlin 

13.  Chicago  16.    Rome  19.    New  York 

14.  San  Francisco  17.    Honolulu  20.    Pittsburg 

21.  When  it  is  midnight  (solar  time)  on  the  last  day  of 
the  year  in  Boston,  how  much  of  the  year  (solar  time) 
remains  to  the  people  of  Honolulu  ? 

22.  The  first  shock  of  the  earthquake  at  Kingston,  Jamaica 
(long.  76°  47'  W.),  Jan.  14,  1907,  occurred  at  3:25  p.m. 
What  was  the  solar  time  at  New  York  ?  at  Cape  Town  ? 

23.  A  ship  sets  sail  from  Liverpool  for  New  York,  Jan. 
10,  1907.  When  in  longitude  34°  6'  10"  W.  its  chronometer 
reads  2:30  p.m.  Jan.  15.  Find  the  difference  in  the  read- 
ings between  the  ship's  time  and  the  meridian  time  of  New 
York. 

24.  Berlin  meridian  time  is  6  hr.  44  min.  and  l\i  sec.  later 
than  Chicago  meridian  time.     Find  the  longitude  of  Berlin. 

101         0      26  difference  in  longitude 
87      36      42  W.  (Chicago) 
101         0      26  13      23      44  E.  (Berlin) 

15  times  the  difference  in  time  expressed  in  hours,  minutes,  and 
seconds  corresponds  to  the  difference  in  longitude  expressed  in  degrees, 
minutes,  and  seconds. 

Therefore,  15  x  6  hr.  44  min.  \\\  sec.  corresponds  to  101°  0'  26"  of 
longitude. 

This  difference  in  longitude  would  not  tell  us  whether  Berlin  is  east  or 
west  of  Chicago,  but  as  Berlin  has  faster  time  than  Chicago,  it  must  be 
east  of  it.  Chicago  is  87°  36'  42"  west  of  the  prime  meridian.  There- 
fore, Berlin  must  be  13°  23'  44"  east  of  the  prime  meridian. 

HAM.    COMPL.     AIMTII. — 23 


hr. 

min. 

sec. 

6 

44 

m 

15 

354  LONGITUDE   AND   TIME 

25.  The  "Treaty  of  Portsmouth"  between  Japan  and 
Russia  was  signed  at  Portsmouth,  N.H.,  Sept.  5, 1905,  at  47 
minutes  past  3  p.m.,  75th  meridian  time.  What  was  the  cor- 
responding solar  time  at  St.  Petersburg,  Russia,  30°  17' 
51"  E.  and  at  Tokyo,  Japan,  139°  44'  30"  E.  ? 

Tokyo  is  east  of  the  75th  meridian  214°  44'  30",  therefore  its  time  is 
14  hr.  18  min.  58  sec.  faster  than  Portsmouth,  which  has  75th  meridian 
time.  Counting  this  time  forward  from  3:47  p.m.  Sept.  5,  gives  5 
minutes  and  58  seconds  past  6  o'clock  a.m.  Sept.  6,  Tokyo  solar  time. 

26.  The  President  of  the  United  States  takes  the  oath  of 
office  at  12  noon,  75th  meridian  time.  Find  the  solar  time 
and  date  in  each  of  the  following  places  for  the  inaugura- 
tion of  March  4,  1909  :  Honolulu ;  Berlin ;  San  Francisco ; 
London. 

International  Date  Line 

The  nations  have  agreed  upon  the  180th  meridian,  with  slight 
changes  as  shown  on  page  355,  as  the  place  where  the  new  day  always 
begins.  The  calendar  is  set  forward  one  day  on  ships  crossing  this  line 
sailing  westward :  the  calendar  is  set  back  one  day  on  ships  crossing  this 
line  sailing  eastivard. 

1.  A  ship  sets  sail  from  San  Francisco  for  Manila,  Oct.  9, 
1906,  at  9  A.M.,  120th  meridian  time;  it  arrives  at  Manila, 
Oct.  27,  at  9  a.m.,  meridian  time.     How  long  is  the  voyage  ? 

2.  The  same  ship  sets  sail  from  Manila,  Nov.  3,  1906,  at 
3  p.m.,  meridian  time,  and  arrives  at  San  Francisco,  Nov.  23, 
at  3  p.m.,  120th  meridian  time.     How  long  is  the  voyage  ? 

Standard  Time 

The  railroads  of  the  United  States  in  1883  agreed  upon 
a  system  of  standard  time  and  divided  our  country  into  four 
time  belts,  as  shown  on  the  map.  In  the  eastern  time  belt- 
all   trains   keep   the   time   of   the   75th   meridian,  known  as 


STANDARD   TIME 


355 


eastern  standard  time.  In  the  central  belt  all  trains  keep 
the  time  of  the  90th  meridian,  known  as  central  standard 
time.  In  the  mountain  time  belt  all  trains  keep  the  time  of 
the  105th  meridian,  known  as  mountain  standard  time.  In 
the  Pacific  time  belt  all  trains  keep  the  time  of  the  120th 
meridian,  known  as  Pacific  standard  time. 

Each  railway  has  selected  the  most  convenient  towns  on  its  route,  as  is 
shown  on  the  map,  to  change  from  the  standard  time  of  one  belt  to  the 
standard  time  of  another  belt.  The  time  in  any  belt  is  1  hour  faster 
than  the  time  in  the  belt  west  of  it,  or  1  hour  slower  than  the  time  in 
the  belt  east  of  it.  Correct  time  is  telegraphed  each  day  to  all  parts  of 
the  United  States  from  the  Naval  Observatory  at  Washington. 


/~*V. pr»ndca 

;  •  .-•      \  —  Vandaa  • 

/  :  u 


Fort 


Minneapolis  '. 
i       < ' 


'peJI"r."1.roag  Pine       _.'.-- 
.    !    V    North    .'■     K^lf 

f    ^*°\ oke f-.McCook   V « 

'  *  'PbillipsTaurt*      ■  .*v 


IV-nv 


^'sco    :' 
O    \\°  L.        °   :    A.    rJV      ' .".---"-.„ :■.■•■;■'   ■St.LpvJS 
\    >    '      "— £. ^vpagc  City*    Hoieington 


£  i 


Dallaa    '• 


STANDARD  TIME 
/  BELTS 


ISO 


y-/'~"\ 


j,  J^O^J  ^few  Orleans 
Galveston 


1.  What  is  the  difference  in  time  between  closing  of  the 
election  polls  at  7  p.m.  in  New  York  and  7  P.M.  Seattle,  on 
the  day  for  choosing  presidential  electors  ? 

2.  A  telegraph  message  was  sent  from  Philadelphia  at  11 
a.m.  Oct.  12,  l!»0*i,  to  San  Francisco  and  delivered  at  7:45 
A.M.  San  Francisco  time.        Why  could  this  be  true? 


GOVERNMENT  LAND  MEASURES 


Surveyor's  square  measure  is  used  by  surveyors  in  measur- 
ing and  computing  land  areas. 


16  square  rods 

=  1  square  chain 

10  square  chains 

=  1  acre 

640  acres 

=  1  square  mile 

36  square  miles 

=  1  township 

The  Gunter's  chain  for  measuring  land  is  gradually  going  out  of  use. 
In  its  place  surveyors  use  a  steel  tape  100  ft.  long,  divided  into  feet  and 
decimal  parts  of  a  foot.  They  find  the  number  of  square  feet  in  the  plot 
to  be  measured,  and  change  the  result  to  acres  by  dividing  by  43560,  the 
number  of  square  feet  in  an  acre. 

The  public  lands  of  the  United 
States  are  surveyed  by  selecting 
a  north  and  south  line,  called  a 
principal  meridian,  and  intersect- 
ing this  by  an  east  and  west 
line,  called  a  base  line. 

Range  lines  are  lines  running 
north  and  south  on  each  side  of 
the  principal  meridian,  at  dis- 
tances of  6  miles.     They  divide 
the  land  into  strips  6  miles  wide, 
called  ranges. 
East  and  west  lines  parallel  to  the  base  line,  and  at  dis- 
tances of  6  miles,  divide  the  ranges  into  townships.     A  range 
is,  therefore,  a  row  of  townships  running  north  and  south. 
The  townships  in  each  range  are  numbered  north  and  south 

356 


A  Group  of  Townships 


<;<)\T.KXMK\T    I. AND    MEASURES 


357 


from  tlir  base  line,  and  the  ranges  are  numbered  cast  and 
west  from  the  principal  meridian. 

A  township  is  designated  by  its  number  and  direction  from 
the  base  line,  the  number  and  position  of  its  range,  and  the 
name  or  number  of  the  principal  meridian.  Tims,  Township 
A  is  4  North,  Range  5  West  of  Principal  Meridian. 


i 

S 

* 

3 

2 

1 

7 

a 

9 

10 

II 

12 

IB 

17 

76 

IS 

It 

13 

19 

20 

21 

22 

23 

24 

.30 

29 

28 

27 

25 

25 

31 

32 

33 

34- 

35 

J6 

W/2 

section 
(320  A) 

n.e.v* 

of 
NE.  '/* 

S.E./* 

of 
NE.'/* 

Eti 

of 
■.:   . 

of 
S£3i 

of 
S.E.'/* 

A  Township 


A  Section 


A  township  is  6  miles  square  and  is  divided  into  30  sec- 
tions each  one  mile  square.     Each  section  contains  640  acres. 

1.  W.  \  Sec.  31,  T.  22  N.,  4  E.  3d  P.  M.  is  read  west  | 
section  31,  township  22  North,  Range  4  east  of  third  princi- 
pal meridian. 

2.  Read:  S.  1  of  S.E.  J,  Sec.  31. 

3.  Read  :  NAY.  \  of  S.E.  J,  Sec.  31. 

4.  Read  :  N.E.  \  of  N.E.  \,  Sec.  31. 

Locate  the  tract  of  land  in  sections  and  give  number  of 
acres: 

5.  SAY.  \,  Sec.  5,  T.  4  S.,  R.  3  W. 

6.  S.l  of  N.E.  l   Sec.  4,  T.  15  N.,  R.  5  E. 

7.  S.E.  \  of  N.W.  {,  Sec.8,  T.  125  S.,  R.  4  W. 

8.  Find  the  number  of  rods  of  fence  required  for  the  tract 
in  problem  7. 

9.  How  many  rods  of  fence  are  required  for  the  tract 
mentioned  in  problem  0  ? 


POWERS  AND  ROOTS 

1.  3x3  =  9.     4x4  =  1G.     5x5x5  =  125. 

2.  Name  the  two  equal  factors  that  produce  9.     16. 

3.  Name  the  three  equal  factors  that  produce  125. 

4.  What  two  equal  factors  produce  25?    36?   49?    81? 

5.  What  three  equal  factors  produce  8?   27?    64? 

6.  How  many  times  is  5  used  as  a  factor  in  5  ?     25  ? 
125? 

7.  How  many  times  is  3  used  as  a  factor  in  3  ?    9  ?     27  ? 

A  power  of  a  number  is  the  product  obtained  by  taking 
the  number  one  or  more  times  as  a  factor.  Thus,  9  is  a 
power  of  3,  and  8  is  a  power  of  2. 

The  first  power  of  a  number  is  the  number  itself.  The 
second  power  of  a  number  is  called  the  square  of  the  number. 
Thus,  16  is  the  square  of  4.  The  third  power  of  a  number  is 
called  the  cube  of  the  number.     Thus,  64  is  the  cube  of  4. 

8.  What  is  the  square  of  4  ?     5  ?     6  ?     7  ?     8  ?     9  ? 

9.  What  is  the  cube  of  2?     3  ?     5  ?     6  ?     7? 

10.  |  x  |  =  |.     What,  then,  is  the  square  of  f  ? 

11.  I  x  |  x  |  =  §£.     What,  then,  is  the  cube  of  f  ? 

12.  .3  x  .3  =  .09.  .5x.5=.25.  What,  then,  is  the 
square  of  .3  ?     of  .5? 

The  square  of  a  fraction  is  found  by  squaring  both  terms,  the 

cube  of  a  fraction  by  cubing  both  terms. 

358 


roots  359 

13.  3x3  =  9.  The  square  of  3  is  indicated  thus,  32; 
4  x  4  x  4  =  64.     The  cube  of  4  is  indicated  thus,  43. 

14.  How  much  is  52?  62?  72?  53?  63  ?  What  is  the 
value  of  (f)2?     (§)3?     .42?     .43?     (2\f! 

An  exponent  is  a  small  figure  placed  at  the  right  of,  and  a  lit- 
tle above  the  number,  to  indicate  the  number  of  times  it  is  to 
be  taken  as  a  factor ;  thus,  43  =  4x4x4  =  64.     Exponent,  3. 

Written  Work 

1.  Square  6,  7,  8,  9,  10,  12,  15. 

2.  Cube  3,  4,  5,  6,  7,  8,  0,  10,  12. 

3.  Square  30,  50,  60,  80,  120. 

4.  Cube  20,  30,  40,  50,  100. 

5.  Find  the  value  of  62,  82,  92,  53,  63,  73. 

6.  Find  the  value  of  (f)2,  (f)3,  (f)2,  (|)3,  (f)2,  (ll)2. 

7.  Square  .3,  .04,  .05,  .6,  .06.     Cube  .4,  .04,  .6. 
Find  the  value  of : 

8.  152  ll.    222  14.    .752 

9.  162  12.     252  15.     (If)2 

io.    182  13.    6.52  16.    (16i)a 

Find  the  number  of  square  units  in  a  surface  whose  side  is: 

17.  15  in.  20.    8  ft.  6  in.  23.    10  yd. 

18.  25  ft.  21.    5  in.  24.    5  yd.  2  ft. 

19.  16  yd.  22.    8.5  in.  25.    0  mi. 
Find  the  number  of  cubic  units  in  a  volume  whose  edge  is: 

26.  8  in.  28.    3  ft.  3  in.  30.    1  yd.  10  in. 

27.  2  ft.  29.    42  in.  31.    12  ft.  4  in. 


360 


POWERS   AND   ROOTS 


EXTRACTING  ROOTS 

A  root  of  a  number  is  one  of  the  equal  factors  that  pro- 
duce that  number.     Thus,  3  is  a  root  of  9. 

The  square  root  of  a  number  is  one  of  its  two  equal  factors. 
Thus,  4  is  the  square  root  of  16. 

The  cube  root  of  a  number  is  one  of  its  three  equal  factors. 
Thus,  4  is  the  cube  root  of  64. 

1.  What  is  the  square  root  of  25  ?  36  ?  49  ?  81  ?  100  ? 

2.  What  is  the  cube  root  of  8  ?    64  ?    125  ?    216  ? 

The  root  of  a  number  is  generally  indicated  by  writing 
the  number  under  the  radical  or  root  sign  -y/~  '  ,  and 
placing  a  figure  called  the  index  in  the  angle  of  the  sign  ; 
thus,  a/27  denotes  the  cube  root  of  27.  The  square  root  is 
indicated  by  V  without  the  index. 

The  root  of  a  fraction  equals  the  root  of  the  numerator  di- 
vided by  the  same  root  of  the  denominator. 

Find  the  required  root :     Thus,  V64  =  V8  x  8  =  8. 
/16 


3. 
4. 
5. 
6. 
7. 


\V27 

a/25 
aV«34 


8. 

9. 
10. 
11. 
12. 


v  100 

V49 


VI 25 

v  125 

a/81 


13. 
14. 
15. 

16. 
17. 


V216 
a/1000 


V343 


V.064 


18. 
19. 
20. 
21. 
22. 


V512 


V144 


V169 


a/2500 


V8100 


Some  perfect  powers  and  their  roots. 

Memorize: 

VI=1  a/36  =  6 

a/4  =  2  a/49  =  7 

a^9=  3  a/64  =  8 

Vl6  =  4  a/81  =  9 

a/25  =  5  a/100  =  10         aVI25  =  5 


aVI  =  1 

aV8  =  2 
a/27  =  3 
aV64  =  4 


a/216  =  6 
a/343  =  7 
aV512  =  8 
a/729  =  9 
a/1000  =  10 


SQUARE   ROOT 


361 


Finding  the  root  of  a  perfect  square  or  cube  by  factoring. 

Written  Work 

1.    Find  the  square  root  of  1225. 

When  factored  1225  =5x5x7x7. 
Arranged  into  two  like  groups  1225  =  (5  x  7)  x  (5  x  7). 

V1225  =  5  x  7,  or  35. 

Find  the  root  of  each  number,  as  indicated,  by  factoring  : 

7.    VT84  12. 

13. 


V225 


V576 
V441 


4. 
5. 
6.     V1600 


V196 


8. 

9. 
10. 
11. 


V1296 


V17G4 
^13824 


V4096 


V2304 

a/42875 


14. 
15. 
16. 


V3136 

a/5832 
a/8000 


17. 
18. 
19. 
20. 
21. 


V5184 

a/15625 

a/32768 


ID!  Hi 


a/19683 


SQUARE  ROOT 

Comparing  roots  and  periods. 

The  squares  of  the  smallest  and  the  largest  integers  com- 
posed of  one,  two,  and  three  figures  are  as  follows  : 

!2=i  102  =  100  1002=  10000 

92  =  8i  992  =  9801  9992  =  998001 

1.  Separate  each  of  these  squares  into  periods  of  two 
figures  each,  beginning  at  the  right  ;  thus,  99'  80'  01. 

2.  How  does  the  number  of  periods  in  each  square  compare 
with  the  number  of  figures  in  the  corresponding  roots  ? 

The  number  of  periods  of  two  figures  each,  beginning  at  units, 
into  which  a  number  can  be  divided  equals  the  number  of 
figures  in  the  root. 

Note.  —  The  left-hand  period  may  contain  only  one  figure. 

3.  How  many  figures  are  there  in  the  square  root  of  4225? 
of  12544?  of  133225?  of  810000? 


362 


POWERS   AND   ROOTS 


Written  Work 

1.  Square  25.     25  =  20  +  5,  hence  it  may  be  squared  in 
two  ways,  thus: 

25  =                         20  +  5  The  square  of  25  has  three  partial 

25  =                         20  +  5  products : 

125^                 20  x  5  +  52  f(l)              202  =  400  1 

500=         2Q2+20x5  252  =     (2)   2(5x20)  =  200  \  =625 

625  =  202  +  2  (20  x  5)  +  52  [  (3) 

2.  Find  the  square  root  of  625. 


52  =  25  J 


6'25 
202  =  4  00 


Trial  divisor,  2  x  20  =  40 

_5 
Complete  divisor,  =  45 


225 


225 


20 

_5 
25 


In  practice: 

6'25  J  25 
4 


45 


225 
225 


mtm 


m 


i 


Since  625  has  two  periods,  its  square  root  is  composed  of  two  figures, 
tens  and  ones.     Since  the  square  of  tens  is  hundreds,  6  hundreds  must  be 

the  square  of  at  least  2  tens.  Two  tens  or  20 
squared  is  400,  as  shown  in  figure  A  ;  and  625  —  400 
leaves  a  remainder  of  225.  The  root  20,  therefore, 
must  be  so  increased  as  to  exhaust  this  remainder 
and  keep  the  figure  a  square. 

The  necessary  additions  to  enlarge  A,  and  keep 
it  a  square,  are  the  two  equal  rectangles  B  and  C, 
and  the  small  square  D. 

B,  C,  and  D  contain  225  square  units ;  and  since 
rj  the  area  of  D  is  small,  if  225  is  divided  by 

40,  the  combined  length  of  B  and  C,  the 
quotient  will  indicate  the  approximate 
width  of  these  additions.  The  quotient  is 
5;  the  entire  length  of  B,  C,  and  D  is 
20  +  20  +  5  =  45  units ;  and  the  area  of  the 
additions  is  5  times  45  x  1  sq.  unit,  or  225  sq. 
units.  Since  these  three  additions  exhaust 
the  remaining  225  sq.  units,  and  keep  the  fig- 
ure a  square,  the  side  of  the  required  square 
is  25  units,  and  the  square  root  of  625  is  25. 


B 


:M 


±t 


20 


$z'z 


SQUA1JK    HOOT 


363 


3.    Square  35(30  +  5);  then  find  the  square  root  of  12:1"). 


Partial 
Products : 


(1)  3o2=900 

(2)  2(5x80)  =300 

(3)  52  =    25 

12'25 

302  9  00 

Trial  divisor,       2  x  30  =  60 

_5 
Complete  divisor,  05_ 


►  1225 

30 
_5 
S3 


Study  of  Problem 

1.  How  many 
periods  in  1225  ? 

2.  How  many 
figures,  then,  will 
be  in  its  root  ? 

3.  What  is  the 
largest  partial 
product  in  1225  ? 

4.  What  is  the 
square  root  of  9<>o? 

5.  What      two 
partial  products  are  contained  in  the  325  remaining? 

6.  325  is  composed  principally  of  which  partial  product?  2(5  x  30). 
325  is  composed  principally  of  2  times  the  first  figure  of  the  mot  by  the 

second.     Hence,    if   325  is  divided  by   (2  x  30),  the  quotient  will   give 
approximately  the  second  figure  of  the  root. 

7.  What  is  the  quotient  ?     What,  then,  is  probably  the  second  figure 
of  the  root? 

8.  What  must  be  added  to  the  trial  divisor  (2  x  30)  to  form  the  com- 
plete divisor? 

Since  5  x  65  =  325,  5  is  the  second  root  figure,  and  30  +  5,  or  35,  is  the 
square  root  of  1225. 

9.  How  does  (5  x  60)  +  (5x5)  compare  with  5  x  65? 

4.    Find  the  square  root  of  21.16.     Separate  the  number 
into  periods,  left  and  right  from  the  decimal  point. 


.    402  = 

'21.16' 
16  00 

4.0 +  .6  = 

4.6 

In  practice  : 
'21.16'  |   4.6 

Trial  divisor,  2  x  40  =  80 

5  16 
5  16 

16 

_6_ 
Complete  divisor,        86 

86 

516 
5  16 

Beginning  <tt  unit*,  separate  the  number  into  periods  of  two 
figures  each. 


364 


POWERS   AND   ROOTS 


Find  the  largest  square  in  the  first  period  on  the  left,  and 
write  its  root  as  the  first  figure  in  the  required  root.  Subtract 
its  square  from  the  period  and  annex  the  second  period  to  the 
remainder. 

Double  the  root  found  for  a  trial  divisor.  Divide  the  re- 
mainder, omitting  the  last  figure,  by  this  trial  divisor,  and 
annex  the  quotient  to  the  trial  divisor  and  also  to  the  root. 

Multiply  the  complete  divisor  by  the  second  figure  of  the  root, 
and  subtract  the  product  from  the  remainder. 

Double  the  root  already  found  for  another  trial  divisor,  and 
proceed  as  above  until  all  the  periods  have  been  used. 

Note.  —  When  a  naught  occurs  in  the  root,  annex  a  naught  to  the 
trial  divisor,  bring  down  another  period,  and  proceed  as  before. 

In  extracting  the  square  root  of  a  decimal  or  a  whole  number  and  a 
decimal,  point  off  into  periods  of  two  figures  each,  the  whole  number 
toward  the  left  and  the  decimal  toward  the  right  of  the  decimal  point. 

In  extracting  the  square  root  of  a  fraction,  extract  the  square  root  of 
the  numerator  and  of  the  denominator  if  both  terms  are  perfect  squares ; 
or  reduce  the  fraction  to  a  decimal,  and  extract  the  root  of  the  decimal. 


Solve  the  following 


5. 

V484 

9.    V1089 

13. 

v  100 

17. 

V.0225 

6. 

V576 

10.    V1849 

14. 

Vi  as. 

v  225 

18. 

V4.41 

7. 

V676 
V96I 

11.    V2601 

15. 
16. 

v  324 

V725 

19. 
20. 

V6.25 

8. 

12.    V3969 

V.0625 

Find  the  square  root  to  the  nearest  hundredth  of 

: 

21. 

315 

26.    178.25 

31. 

96.8256 

36. 

.8464 

22. 

525 

27.    14884 

32. 

192ft 

37. 

.012996 

23. 

1156 

28.    26569 

33. 

540JL 

38. 

.000566 

24. 

4356 

29.    136161 

34. 

31921 

39. 

.43681 

25. 

210.25 

30.    20.7936 

35. 

5643|| 

40. 

112225 

THE    RIGHT   TRIANGLE 


365 


The  hypotenuse  <>f  a  right  tri- 
angle is  the  side  opposite  the  right 
angle. 

1.  How  many  square  units  are 
there  in  the  square  described  upon 
the  hypotenuse '!  in  the  square 
described  upon  the  perpendicular? 
in  the  square  described  upon  the 
base  ? 

2.  How  do  the  number  of  square 
units  described  upon  the  hypotenuse  compare  with   the  gum 
of  the  square  units  described  upon  the  other  two  sides  ? 

That  this  is  universally  true  is  shown  by  the  following  diagram  : 


iri 


5 

3 

\     4 


Take  any  right  triangle,  as  1;  lay  it  off  on  a  piece  of  cardboard  and 
draw  the  square  on  its  hypotenuse.  Cut  this  square  into  the  four  equal 
triangles  1,  2,  3,  and  4,  and  the  small  square  5.  as  here  shown. 

By  changing  the  position  of  the  triangles  1  and  2  as  indicated,  we 
change  the  first  diagram  into  the  second.  But  the  first  is  the  square  on 
the  hypotenuse,  and  the  second  is  the  sum  of  the  squares  on  the  other  two 
sides.     Since  they  are  equal,  the  truth  of  the  proposition  is  evident. 

The  square  on  the  hypotenuse  of  a  right  triangle  equals  the 
sum  oj  thesquar*  *  described  on  the  other  two  sides. 


366  POWERS   AND   ROOTS 

Written  Work 

1.    Find  the  hypotenuse  of  this 
right  triangle. 

Hypotenuse2  =  W2  +  602,  or  4756 
Hypotenuse  =  V4756  =  68.9  +  ft. 

60  ft.  ~ 

Draw  figures  to  a  convenient  scale  and  find  the  unknown 

side : 

Base  Perpendicular  Hypotkxuse 

2.  18  in.  27  in.  (x) 

3.  (a;)  4  ft.  5  ft. 

4.  24  ft.  (a;)  40  ft. 

5.  15  yd.  20  yd.  (x) 

6.  (x)  40  in.  60  in. 

7.  Find  the  length  of  the  longest  straight  line  that  can 
be  drawn  on  a  table  8  ft.  by  4  ft. 

8.  A  has  a  field  40  rd.  long  and  30  rd.  wide.  B  has  a 
square  field  whose  side  equals  the  diagonal  of  A's  field. 
What  is  the  difference  in  the  area  of  the  two  fields  ? 

9.  Find  the  longest  straight  line  in  a  room  16  ft.  in 
length  by  12  ft.  in  width  by  10  ft.  in  height. 

10.  Two  automobiles,  A  and  B,  start  from  the  same  point. 
A  goes  east  10  mi.,  then  north  10  mi. ;  B  goes  west  20  mi., 
then  south  20  mi.     Draw  figure  and  find  distance  apart. 

11.  Find  the  length  of  the  diagonal  of  a  square  field  con- 
taining 225  sq.  rd. 

12.  Find  the  side  of  the  largest  square  that  may  be  in- 
scribed in  a  circle  2  ft.  in  diameter. 

13.  A  fireman's  ladder  just  reaches  a  window  36  ft.  above 
the  ground.  How  long  is  the  ladder  if  its  foot  is  27  ft.  from 
the  building? 


MENSURATION 

Rectangular  surfaces,  rectangular  solids,  and  the  cylinder 
have  been  treated  under  Practical  Measurements. 


REGULAR   POLYGONS 

A  plane  is  a  surface  such  that  a  straight  line  joining  any 
two  of  its  points  lies  wholly  in  the  surface. 

A  polygon  is  a  plane  figure  bounded  by  straight  lines. 

A  regular  polygon  is  a  plane  figure  having  equal  sides  and 
equal  angles. 


Triangle 


Square 


Pentagon 


Hexagon 


Polygons  are  named  from  their  sides.  A  regular  polygon  of  three 
sides  is  called  an  equilateral  triangle;  one  of  four  sides,  a  square;  one 
of  Jive  sides,  a  pentagon ;  one  of  six  sides,  a  hexagon,  etc. 

Finding  the  area  of  a  regular  polygon. 

Draw  a  circle.  Divide  the  circumference  into  6 
equal  parts  by  points  marked  at  distances  apart 
equal  to  the  length  of  the  radius.  Join  these  points, 
thus  making  a  hexagon.  Connect  the  opposite 
points  by  dotted  lines,  thus  dividing  the  hexagon 
into  six  equilateral  triangles. 

Show  by  folding  together  the  opposite  sides  of 
any  equilateral,  and  the  equal  sides  of  any  isosceles  triangle,  that  each 
may  be  divided  into  two  equal  right  triangles. 

The  area  of  any  regular  polygon  equals  the  sum  of  the  areas 
of  the  triangles  composing  it. 


3G8 


MENSURATION 


•  1.  Find  the  surface  of  the  bottom  of  a  hexagonal  silo  that 
is  12  feet  on  a  side,  the  distance  from  the  middle  point  of  the 
side  to  the  center  of  the  bottom  being  10.3  ft. 

2.  How  far  from  the  corner  is  the  center  of  a  square  field 
that  is  40  rods  on  a  side?     (Draw  the  figure.) 

3.  Find  the  area  of  an  equilateral  triangular  design  that 
is  15  inches  on  a  side.     (Divide  into  two  right  triangles.) 


SOLIDS 

A  solid  is  anything  that  has  length,  breadth,  and  thickness. 

The  faces  of  a  solid  are  the  surfaces  that  bound  it. 

The  lateral  or  convex  surface  of  a  solid  is  the  area  of  its 
sides,  or  faces. 

The  volume  of  a  solid  is  the  number  of  cubic  units  it  con- 
tains. 

A  prism  is  a  solid  whose  ends  are  equal  and  parallel  poly- 
gons, and  whose  sides  are  parallelograms.  Prisms  are  named 
from  their  bases,  as  triangular,  square,  rectangular,  pentagonal, 
hexagonal,  etc. 


Triangular 
Prism 


Square 
Prism 


Pentangular  Prism    Rectangular  Prism 


A  cylinder  is  a  solid  with  circular  ends  and  uniform 
diameter.  The  ends  are  the  bases,  and  the  curved  surface 
is  the  convex  surface. 

The  altitude  of  a  prism  or  of  a  cylinder  is  the  perpendicu- 
lar distance  between  the  bases. 


SI'IMWCKS    OF    SOLIDS 


3fi0 


Cylinder 


A  pyramid  is  a  solid  whose 
base  is  a  regular  polygon,  and 
whose  faces  are  triangles  that 
meet  at  a  point  called  the  vertex. 
Pyramids  are  named  from  their 
bases,  as,  triangular,  square,  pen- 
tagonal, etc. 

Pyramid 

The  slant  height  of  a  pyramid  is  the  altitude 
of  the  triangles  that  bound  it. 

A  cone  is  a  solid  whose  base  is  a  circle,  and 
whose  convex  surface  tapers  uniformly  to  a 
point  called  the  vertex. 

The  altitude  of  a  pyramid,  or  of  a  cone,  is  the 
perpendicular  distance  from  the  vertex  to  the 
base. 

The    slant  height  of  a  cone   is  the  distance  between  the 
vertex  and  any  point  in  the  circumference  of 
the  base. 

A  globe  or  sphere  is  a  solid  bounded  by 
a  curved  surface,  every  point  of  which  is 
equally  distant  from  a  point  within,  called 
the  center.  sphere 


Cone 


SURFACES  OF  SOLIDS 


Surfaces  of  Prisms  and  Cylinders 

Observe :  1 .  That  if  a  piece  of  paper  is 
fitted  to  cover  the  convex  surface  of  a  prism 
or  a  cylinder,  and  then  unrolled,  its  form  will 
be  that  of  a  rectangle,  as  ABCD. 

2.  That  the  perimeter  of    the   solid  forms 
one   side  of    the  rectangle,   and  the    altitude  of  the   solid   the  other 
side. 

HAH.    COMPL.    AKITII.  — 24 


370 


MENSURATION 


q  The  convex  surface  of  a  prism 
or  of  a  cylinder  is  found  by  multi- 
plying the  unit  of  measure  by  the 
product  of  the  perimeter  and  the 

S     altitude. 

Find  the  convex  surface  of  a  regular  prism  of : 

1.  5  sides  ;   1  side  10  ft. ;   height  5  ft. 

2.  3  sides  ;  1  side  20  in. ;  height  42  in. 

3.  A  steam  boiler,  diameter  3  ft.  ;  length  10  ft.     Entire 
surface  =  ? 

4.  A  water  pail,  diameter  11  in. ;  height  15  in.     Entire 
surface  =  ? 

Surfaces  of  Pyramids  and  Cones 

Observe  :  1.  That  the  convex  surface  of  a  pyramid  is  composed  of 
triangles. 


Pyramid 


Cone 


2.  That  the  convex  surface  of  a  cone  may  also  be  considered  as  made 
up  of  small  triangles. 

3.  That  the  bases  of  the  triangles  in  both  pyramid  and  cone  form  the 
perimeter  of  the  base  of  the  figure,  and  the  altitude  of  the  triangles  the 
slant  height.     Hence, 

TJie  convex  surface  of  a  pyramid  or  of  a  cone  is  found  by 
multiplying  the  unit  of  measure  by  one  half  the  product  of  the 
perimeter  and  the  slant  height. 


CYLINDER    AND  SPHERE 


371 


Find  the  convex  surface  of  a  pyramid  or  a  cone  if  : 

1.  Diameter  of  base  of  cone  =  9  ft. ;  slant  height  =  12  ft. 

2.  One  side  of  a  square  pyramid  =  16  ft. ;  slant  height  = 
24  ft. 

3.  One  side  of  a  square  pyramid  =  5  ft.;  altitude  = 
16  ft. 

4.  Altitude  of  square  pyramid  =  24  ft. ;  one  side  =  14  ft. 

5.  A  church  spire  is  in  the  form  of  a  hexagonal  pyramid, 
each  side  being  10  feet,  and  the  slant  height  65  feet.  Find 
the  cost  of  painting  it  at  25^  per  square  yard. 

6.  A  spire  on  the  corner  of  a  church  is  in  the  form  of  a 
cone.  Its  base  is  12  feet  in  diameter  and  its  slant  height  24 
feet.  Find  the  cost  of  covering  it  with  tin  at  $13  per 
square  (100  sq.  ft.  =  1  square). 

Comparative  Surfaces  of  Cylinder  and  Sphere 


Examine  the  solids.  What  is  the  height  of  the  cylinder?  What  is 
the  diameter  of  the  cylinder?  What  is  the  diameter  of  the  sphere? 
How  does  the  diameter  of  each  compare  with  the  height  of  the  cylinder? 
Observe  that  the  dimensions  are  equal. 

Geometry  shows  that  the  surface  of  a  sphere  is  equal  to  the  convex 
surface  of  a  cylinder  wThose  height  and  diameter  are  each  equal  to  the 
diameter  of  the  sphere. 


372 


MENSURATION 


To  show  this,  wind  a  hard  wax  cord  around  a  cylinder  1  in.  in  height 
and  1  in.  in  diameter  until  its  convex  surface  is  covered.  Unwind  the 
cord  from  the  cylinder  on  to  a  sphere  1  in.  in  diameter  as  shown  in  the 
illustration.  When  one  half  the  surface  of  the  sphere  is  covered  with 
the  cord,  one  half  of  the  convex  surface  of  the  cylinder  is  uncovered. 
Hence, 

The  surface  of  any  sphere  equals  the  convex  surface  of  a 
cylinder  of  equal  dimensions. 

It  may  also  be  shown  by  geometry  that 

The  surface  of  a  sphere  equals  the  square  of  the  diameter 
multiplied  by  3.1416,  or  ttcP  (representing  the  diameter  by  d 
and  3.1416  by  7r). 


Find  the  surface  of  : 

1.  A  globe,  D.  12  in. 

2.  A  ball,  R.  l-i-  in. 


3.  A  sphere,  Z>.  13  in. 

4.  A  ball,  I).  4  in. 

5.    How  much  will  it  cost  to  paint  a  dome  in  the  form  of  a 
hemisphere,  20  ft.  in  diameter,  at  25  cents  per  square  yard  ? 

VOLUME  OF  SOLIDS 
Prisms  and  Cylinders 


-Niif 


Scale  \  in.  =  1  in. 

Observe  :  1.    That  the  solids  are  all  4  in.  high. 

2.  That  the  first  row  in  the  rectangular  prism  contains  4  cu.  in. 

3.  That  if  the  first  row  in  each  solid  contains  4  cu.  in."  the  volume  of 
each  solid  is  4  times  4  cu.  in.,  or  16  cu.  in. 


PYRAMIDS    AND    CONES 


373 


The  volume  of  a  prism  or  of  a  cylinder  is  found  by  multiplying 
the  unit  of  measure  by  the  product  of  the  numbers  corresponding 
to  the  area  of  the  base  and  the  altitude. 

Find  the  volume  of  : 

1.  A  prism  4  inches  square  ;   altitude  8  inches. 

2.  A  square  prism,  side  12  in.;  altitude  24  in. 

3.  A  hexagonal  silo  is  25  ft.  high,  12  ft.  on  a  side,  and 
10.3  ft.  from  the  middle  point  of  a  side  (measuring  at  the 
base)  to  the  center  of  the  base.  Estimating  50  cu.  ft.  to  a 
ton  of  ensilage,  how  many  tons  will  the  silo  contain  ? 

4.  In  the  rotunda  of  a  building  there  are  6  cylindrical  mar- 
ble columns,  18  in.  in  diameter  and  18  ft.  in  height.  Esti- 
mate the  number  of  cubic  feet  in  all. 


PYRAMIDS    AND    CONES 

1.  Fill  a  hollow  pyramid  with  sand.  Empty  it  into  a 
prism  having  the  same  base  and  altitude.  How  often  must 
the  pyramid  be  filled  and  emptied  to  fill  the  prism  ?  The  vol- 
ume of  a  pyramid,  then,  is  what  part  of  the  volume  of  the 
prism  ? 


2.  Measure  in  like  manner  with  a  cone  the  volume  of  a 
cylinder  having  the  same  dimensions.  The  volume  of  the 
cone  is  what  part  of  the  volume  of  the  cylinder  ? 


374  MENSURATION 

Observe :  1.  That  the  dimensions  of  the  pyramid  and  of  the  prism  are 
the  same,  and  that  those  of  the  cone  and  of  the  cylinder  are  the  same. 

2.  That  the  volume  of  the  pyramid  is  \  that  of  the  prism,  and  the 
volume  of  the  cone  is  |  that  of  the  cylinder. 

By  geometry,  it  is  shown  that  the  volume  of  a  pyramid  is 
^  of  that  of  a  prism  having  an  equal  base  and  an  equal  alti- 
tude.    Hence, 

The  volume  of  a  pyramid  equals  one  third  of  the  volume  of  a 
prism  of  like  dimensions. 

The  volume  of  a  cone  equals  one  third  of  the  volume  of  a 
cylinder  of  like  dimensions. 

But  we  have  already  learned  that  the  volume  of  a  prism 
or  of  a  cylinder  is  found  by  multiplying  its  unit  of  measure 
by  the  product  of  the  area  of  its  base  by  its  altitude.     Hence, 

The  volume  of  a  pyramid  or  of  a  cone  is  found  by  multiply- 
ing its  unit  of  measure  by  one  third  the  product  of  the  altitude 
and  the  area  of  the  base. 

1.  Find  the  volume  of  a  cone  whose  altitude  is  12  in.  and 
the  diameter  of  the  base  8  in. 

2.  How  often  can  a  conical  cup  8  in.  high  and  6  in.  in  di- 
ameter be  filled  from  a  cylindrical  vessel  2  ft.  high  and  6  in. 
in  diameter? 

3.  Find  the  volume  of  a  pyramid  whose  base  is  12  in. 
square  and  whose  altitude  is  30  in. 

4.  A  square  pyramid  whose  side  is  18  in.  is  32  in.  high. 
Find  its  volume. 

5.  Find  the  volume  of  a  pyramid  whose  altitude  is  12  ft. 
and  whose  base  is  a  square  8  ft.  on  a  side. 

6.  Find  the  contents  of  a  rectangular  pyramid  15  ft. 
high,  the  sides  of  whose  base  are  10  ft.  and  12  ft.  respectively. 

7.  A  pile  of  grain  in  the  form  of  a  cone  is  15  ft.  in  diameter 
and  G  ft.  high.    How  many  bushels  of  grain  does  it  contain  ? 


SPHERES  375 

8.  A  concrete  mixer,  6  ft.  from  base  to  apex,  being  coni- 
cal in  form,  and  measuring  3  feet  across  the  base,  is  filled 
six  times  an  hour.  How  many  cubic  feet  of  concrete  mate- 
rial may  be  manufactured  with  it  in  a  week  of  six  working 
days  of  8  hours  each  ? 

9.  A  wooden  hopper  supplying  coal  to  a  furnace  is  in  the 
form  of  an  inverted  pyramid.  If  it  is  8  ft.  deep  and  6  ft. 
square  at  the  top,  how  many  tons  of  hard  coal  will  it  contain  ? 

10.  A  square  pyramid,  the  perimeter  of  whose  base  meas- 
ures 64  inches,  contains  2048  cubic  inches.     Find  its  altitude. 

11.  The  contents  of  a  cone  are  471.24  cu.  ft. ;  the  altitude 
is  18  ft.     Find  the  diameter. 

SPHERES 

Examine  the  figure: 

Observe :  1.  That  the  solids  formed 
by  the  dissected  part  of  the  sphere  are 
pyramids. 

2.  That  the  radius  of  the  sphere  is 
the  altitude  of  the  pyramids. 

3.  That  the  combined  bases  of  the  pyramids  form  the  convex  surface 
of  the  sphere. 

The  volume  of  a  sphere  is  found  by  multiplying  its  unit  of 
measure  by  one  third  the  product  of  the  radius  and  its  convex 
surface. 

It  is  also  shown  by  geometry  that 

The  volume  of  a  sphere  equals  four  thirds  of  the  cube  of  the 
radius  multiplied  by  3.1416,  or  {representing  the  radius  by  r 
and  3.1416  by  tt)^^. 

Find  the  volume  of  : 

1.  A  globe  12  inches  in  diameter. 

2.  A  bowling  ball  with  a  radius  of  4  inches. 

3.  A  cannon  ball  with  a  diameter  of  8.2  inches. 


376 


MENSURATION 


Comparative  Volumes  of  Cone,  Sphere,  and  Cylinder 


-/-"--- 


w. /'i — _J      I /': 


Compare  the  diameters  of  the  bases  and  the  altitudes  of  the  cone  and 
the  cylinder  with  each  other,  and  with  the  diameter  of  the  sphere.  Ob- 
serve that  the  dimensions  are  all  equal. 

By  geometry  it  is  shown  that  the  volumes  of  these  three 

solids  are  in  the  ratio  of  1,  2,  and  3.    The  volume  of  the  cone 

is  ^,  and  of  the  sphere  §  of  that  of  the  cylinder. 

SIMILAR   SURFACES 
Similar  figures  are  plane  surfaces  that  have   exactly  the 
same  shape,  but  differ  in  size.     Point  out  similar  figures: 


V 

C\J 

<M 

2" 


SIMILAR   SURFACES 


377 


Kl 

<M 


St 


Find  the  areas  of  the  similar  surfaces  on  p.  376.  Square 
the  corresponding  lines  of  the  similar  figures  and  express  their 
ratio.  Compare  the  ratio  of  the  areas  of  the  similar  figures 
with  the  ratio  of  the  squares  of  their  corresponding  lines. 

In  the  similar  figures  observe : 

1.  That  the  cor- 
responding sides 
are  proportional ; 
that  is,  2:4::  3:6. 

2.  That  the  ra- 
tio of  their  areas 
equals  the  ratio  of 

the  squares  of  their  corresponding  lines  ;  that  is,  6  sq.  in.  :  24  sq.  in.  as 
22:42,  oras32:62. 

Corresponding  lines  of  similar  plane  surfaces  are  proportional. 

The  areas  of  similar  plane  figures  are  proportional  to  the 

squares  of  their  corresponding  lines. 

Written  Work 

1.  If  a  rectangle  is  20  ft.  by  50  ft.,  what  will  be  the 
length  of  a  similar  rectangle  30  ft.  in  width  ? 

2.  The  side  of  a  square  field  is  40  rods.  Find  the  side  of 
a  similar  field  that  contains  four  times  as  many  acres. 

3.  A  lady  buys  two  rugs,  one  6  ft.  by  9  ft.  and  a  similar 
rug  18  ft.  in  length.     Find  its  width. 

4.  In  East  Park  a  circular 
fountain  is  40  ft.  across  and  in 
West  Park  a  circular  fountain 
is  26  ft.  across.  The  area  of 
the  first  fountain  is  how  many 
times  the  area  of  the  second 
fountain  ? 

5.  Find  the  length  of  the 
side  marked  x  in  the  larger  of  these  similar  triangles. 


4ft 


378 


MENSURATION 


<■ 


6.    It    costs  119.50  to  gild  a  sphere  18  inches  in  diame- 

-^fe.  ter.  At  the  same  rate  estimate 
the  cost  of  gilding  a  sphere  12 
inches  in  diameter.  Why  are  the 
surfaces  of  all  spheres  similar? 

7.    A  telephone  pole  and  a  lamp 
post  cast  shadows  as  shown  in  the 

S8ft.  fl [j       figure.     Find  the   height  of    the 

24  ft  telephone  pole. 


X 


SIMILAR  SOLIDS 

Similar   solids   are   solids  that  have  the  same  shape   but 
differ  in  contents  or  volume  ;  thus, 


Observe :  1 .  That  the  length  of  the  first  solid  is  to  the  length  of  the 
second  as  1  : 2,  and  that  the  heights  and  widths  of  the  solids  are  in  the 
same  ratio. 

2.  That  the  ratio  of  their  contents  or  volume  equals  the  ratio  of  the 
cubes  of  their  corresponding  lines ;  that  is,  2  cu.  in. :  16  cu.  in.  as  l3 :  23; 
or  as  23 :  43. 

The  corresponding  lines  of  similar  solids  are  proportional. 
The  contents  or  volumes  of  similar  solids  are  proportional  to 
the  cubes  of  their  corresponding  lines. 

Written  Work 
1.    Compare  in  volume  a  5-in.  cube  with  a  10-in.  cube. 


SPECIFIC   GRAVITY  370 


Compare  in  volume: 

2.  A  (ij-imh  globe  with  a  25-inch  globe. 

3.  A  3^-inch  cube  with  a  25-inch  cube. 

4.  A  l(>f-inch  sphere  with  a  50-inch  sphere. 

5.  What  are  corresponding  lines  in  spheres?  in  triangles  ? 

6.  The  dimensions  of  a  rectangular  solid  are  30  ft.  by 
20  ft.  by  12  ft.  What  are  the  dimensions  of  a  similar  solid 
20  ft.  in  length  ? 

7.  A  village  has  two  similar  cylindrical  water  tanks,  one 
15  ft.  in  diameter  and  24  ft.  high;  the  other  10  ft.  in  di- 
ameter.    Find  the  height  of  the  second  tank. 

8.  Make  three  problems  with  similar  rectangular  solids. 

9.  The  volume  of  a  sphere  is  1600  cu.  in.  What  is  the 
volume  of  a  sphere  with  one  half  the  diameter  ? 

10.    A  rectangular  bin  8  ft.  long  contains  92  bu.  of  wheat. 
How  many  bushels  will  a  similar  bin  10  ft.  long  contain  ? 

SPECIFIC  GRAVITY 

1.  A  piece  of  timber  12  inches  square  and  6  feet  long 
floating  in  water  shows  2  inches  of  the  log  above  water. 
How  many  cubic  feet  of  the  log  are  under  water  ?  How 
many  cubic  feet  of  water  are  displaced  by  the  log  ? 

2.  A  cubic  foot  of  water  weighs  62|  lb.  How  many 
cubic  feet  of  water  will  a  log  displace  that  weighs  250  lb.  ? 
If  the  log  in  problem  1  is  §  as  heavy  as  the  same  volume  of 
water,  how  much  of  the  log  is  under  water  ? 

Every  ohject  floating  in  water  displaces  its  own  weight  of 
water. 

Every  object  that  sinks  in  water  displaces  its  own  volume  of 
water. 


380  MENSURATION 

3.  A  piece  of  wood  when  floating  is  |  under  water.  The 
ratio  of  the  weight  of  the  wood  to  the  weight  of  an  equal 
volume  of  water  is  therefore  1  ^  2  or  ^.  What  is  the  ratio 
of  the  weight  of  objects  to  the  weight  of  the  same  volume 
of  water  if  the  displacement  is  \  ?  §  ?  |  ?  f  ?  .5  ? 

Copper  is  8.9  times  as  heavy  as  an  equal  volume  of 
water.  The  ratio  of  the  weight  of  copper  to  the  weight  of 
an  equal  volume  of  water  is,  therefore,  8.9. 

Specific  gravity  is  the  ratio  of  the  weight  of  any  substance 
to  the  weight  of  an  equal  volume  of  water. 

A  cubic  foot  of  water  weighs  62^  pounds  or  1000  ounces. 

4.  The  specific  gravity  of  ice  is  .92.  Find  the  weight  of 
a  block  of  ice  2'  by  18"  by  12". 

5.  The  specific  gravity  of  pure  cows'  milk  is  1.03.  Find 
the  weight  of  50  gallons  of  milk. 

6.  The  specific  gravity  of  cork  is  .24.  Find  the  weight 
of  10  cu.  ft.  of  cork. 

7.  The  specific  gravity  of  lead  is  11.3.  Find  the  weight 
of  20  bars  16"  long,  4"  wide,  and  2"  thick. 

Find  the  weight  of  1  cu.  ft.  of  each  object  whose  specific 
gravity  is  given  : 


8. 

Silver 

10.50 

16. 

Copper       8.90 

9. 

Milk 

1.03 

17. 

Lead         11.30 

10. 

Ice 

.92 

18. 

Sandstone  2.90 

11. 

Nickel 

8.90 

19, 

Iron            7.80 

12. 

Granite 

2.70 

20. 

Tin             7.29 

13. 

Mercury 

13.59 

21. 

Steel          7.83 

14. 

Gold 

19.30 

22. 

Marble       2.70 

15. 

Cork 

.24 

23. 

Ivory           1.83 

REVIEW   OF   MENSURATION  :M 

REVIEW    OF    MENSURATION 

1.  From  an  artesian  well  2  inches  in  diameter  the  water 
flows  out  at  the  rate  of  1|  ft.  per  second.  Find  the  number 
of  barrels  that  flow  out  per  hour. 

2.  One  cubic  inch  of  gold  could  be  pounded  into  how 
many  square  inches  of  gold  leaf  ^^  of  an  inch  in  thickness  ? 

3.  A  spherical  ball  must  be  how  large  in  order  that  a  cube, 
each  surface  of  which  contains  36  square  inches,  could  be  cut 
from  it  ? 

4.  A  copper  ingot  containing  1  cubic  foot  is  to  be  drawn 
into  a  copper  wire  ^  of  an  inch  in  diameter.  Find  the  length 
of  the  wire  when  drawn. 

5.  A  plowman  found  by  measurement  that  he  had  plowed 
a  strip  4  rd.  in  width  around  a  rectangular  field  40  rd.  long 
and  20  rd.  wide.  Find  the  number  of  acres  he  had  plowed. 
Draw  figure  to  illustrate. 

6.  A  western  farmer  has  a  pile  of  corn  in  the  ear,  400  ft. 
long.  The  pile  at  the  end  is  in  the  form  of  an  isosceles  tri- 
angle, 12  ft.  wide  at  the  bottom,  and  the  altitude  of  the  pile 
is  6  ft.  Find  the  number  of  bushels,  allowing  If  cu.  ft.  to  a 
bushel. 

7.  A  solid  ball  6  inches  in  diameter  is  in  a  cylinder  10 
inches  in  diameter  and  10  inches  high.  How  many  cubic 
inches  of  water  will  the  cyclinder  contain  ? 

8.  What  is  the  convex  surface  of  a  piece  of  stove  pipe 
2  feet  long  and  8  inches  in  diameter  ? 

9.  The  inside  diameter  of  a  hollow  globe  is  If  ft.  How 
many  gallons  of  water  will  it  contain  ? 

10.  The  flow  of  water  from  the  same  source  through  two 
different  pipes  depends  upon  the  area  of  the  cross  section  of 
the  openings.  Cm  pare  the  flow  through  a  i-inch  pipe  with 
the  flow  through  a  |-inch  pipe. 


METRIC   SYSTEM   OF   WEIGHTS  AND 
MEASURES 

By  the  United  States  system  of  money  we  may  write  5 
dollars,  9  dimes,  and  7  cents  thus,  $5.97,  because  there  is 
a  uniform  ratio  between  the  dollar  and  the  dime,  the  dollar 
and  the  cent,  the  dollar  and  the  mill ;  the  dollar  being  10 
times  the  dime,  100  times  the  cent,  and  1000  times  the  mill. 

As  a  mill  is  y^j  of  a  dollar,  a  cent  TJo  of  a  dollar,  and  a  dime  ^  of 
a  dollar,  United  States  money  is  based  on  a  decimal  system. 

By  the  English  long  measure,  12  in.  =  1  ft.,  3  ft.  =  1  yd., 
and  5^  yd.  =  1  rd.  ;  thus,  we  see  there  is  no  uniform  ratio 
between  the  rod  and  the  yard,  the  rod  and  the  foot,  and  the 
rod  and  the  inch,  the  rod  being  5|  times  the  yard,  16|  times 
the  foot,  and  198  times  the  inch. 

By  the  English  measure  of  weights,  16  oz.  =  1  lb.,  100  lb. 
=  1  cwt.,  20  cwt.  =  1  ton.  The  ton  equals  20  times  the 
hundredweight,  2000  times  the  pound,  and  32000  times  the 
ounce. 

The  metric  system  was  devised  by  the  French  govern- 
ment in  an  effort  to  establish  a  system  of  weights  and  meas- 
ures that  would  be  on  a  uniform  decimal  scale,  so  that  a 
unit  of  one  denomination  might  be  changed  to  a  unit  of 
another  denomination  by  simply  moving  the  decimal  point. 

The  meter  is  the  fundamental  unit  of  the  metric  system.  Its  length 
(about  39.37  in.)  was  meant  to  be  .0000001  of  the  distance  from  the 
equator  to  the  pole.  Though  an  error  has  since  been  discovered  in  the 
measurement  of  the  distance  from  the  equator  to  the  pole,  the  standard 
unit  has  not  been  changed.  The  original  standard  is  a  bar  of  platinum 
39.37  inches  in  length,  deposited  in  the  archives  in  Paris. 

382 


METRIC  SYSTEM  383 

From  the  meter  every  other  unit  of  measure  or  weight  is 
derived.  Thus,  the  unit  of  weight  is  the  gram,  which  equals 
the  weight  of  1  cubic  centimeter  of  pure  water. 

Draw  a  cube  .01  of  a  meter  on  an  edge  and  state  the 
length  of  the  edge  in  inches. 

The  unit  of  capacity  is  the  liter  (leter),  which  contains  1 
cubic  decimeter. 

Draw  a  cube  .1  of  a  meter  on  an  edge  and  state  the  length 

of  the  edge  in  inches. 

The  metric  system  is  now  in  use  in  most  of  the  civilized  countries 
except  Great  Britain  and  the  United  States,  and  in  the  latter  it  is  in 
use  in  some  of  the  departments  of  the  government.  It  is  the  official 
system  adopted  by  Congress  for  our  island  possessions.  It  is  univer- 
sally used  by  scientists.  The  United  States  by  a  vote  of  Congress  per- 
mitted its  use  in  I860. 

Observe : 

The  meter  measures  length. 

The  square  meter  measures  surface. 

The  cubic  meter  measures  solids  or  volume. 

The  gram  measures  weight. 

The  liter  measures  capacity. 

Latin  prefixes. 

To  express  .1  of  a  meter,  .1  of  a  gram,  and  .1  of  a  liter,  we 
prefix  deci  to  each  of  the  words,  meter,  gram,  and  liter. 
Thus,  decimeter  means  -^  of  a  meter  ;  decigram,  -^  of  a  gram  ; 
and  deciliter,  -^  of  a  liter. 

To  express  .01  of  a  meter,  gram,  and  liter,  we  prefix  centi 
to  each  of  the  words,  meter,  gram,  and  liter. 

To  express  .001  of  a  meter,  gram,  and  liter,  we  prefix  milli 
to  each  of  the  words,  meter,  gram,  and  liter. 

Note.  —  From  these  Latin  prefixes  we  get  our  words  dime,  cent,  and 
mill. 


384 


METRIC   SYSTEM 


Greek  prefixes. 

To  express  10  times  a  meter,  10  times  a  gram,  and  10  times 
a  liter,  we  prefix  deca  to  each  of  the  words,  meter,  gram, 
and  liter.  Thus,  decameter  means  10  times  a  meter  ;  deca- 
gram, 10  times  a  gram ;  and  decaliter,  10  times  a  liter. 

To  express  100  times  a  meter,  gram,  and  liter,  we  prefix 
hecto  to  each  of  the  words,  meter,  gram,  and  liter. 

To  express  1000  times  a  meter,  gram,  and  liter,  we  prefix 
kilo  to  each  of  the  words,  meter,  gram,  and  liter. 

METRIC  MEASURES  OF  LENGTH 
Comparison  of  Fundamental  Units  of  Measures  of  Length 


i  i  I  i  i  i  I  i  i  i  \2 

24 

36 

1  Yard. 

hum 
/ 

2 

3 

4 

5 

6 

7 

8 

9 

10 

I  Meter 
Table  of  Long  Measures 


1  millimeter  (mm.) 

=  .001  of  a  meter 

1  centimeter  (cm.) 

=  .01  of  a  meter 

1  decimeter  (dm.) 

=  .1  of  a  meter  (nearly  4 

in 

) 

1  meter 

=  39.37  in. 

1  decameter  (Dm.) 

=  10  meters 

1  hectometer  (Hm.) 

=  100  meters 

1  kilometer  (Km.) 

=  1000  meters  (nearly  .6 

mi 

.) 

In  metric  long  measure  10  times  one  unit  of  any  denomi- 
nation equals  one  unit  of  the  next  higher  denomination. 

The  denominations  most  frequently  used  are  given  in 
black-faced  type. 


MEASURES  OF   LENGTH  385 

Approximately  : 

1  yard  =  \\  meter  1  mile  =  1.6  kilometer 

The  kilometer  is  used  for  measuring  long  distances;  the 
meter,  for  short  distances  and  for  measuring  cloth,  etc. ;  and 
the  millimeter  is  used  in  the  sciences  and  to  show  veiy  small 
measurements,  as  the  thickness  of  wire,  etc. 

Written  Work 

1.  What  decimal  parts  of  a  meter  are  expressed  by  the 
Latin  prefixes  ?  What  multiples  are  expressed  by  the  Greek 
prefixes  ? 

2.  Draw  a  line  one  meter  long.  Show  the  number  of 
decimeters  in  a  meter ;  the  number  of  centimeters ;  the 
number  of  millimeters. 

3.  Explain  why  5m.  =  50  dm.  =  500  cm.  =  5000  mm. 

4.  In  the  metric  S3'stem  the  fundamental  operations  are 
decimal  or  multiple  operations.  .  Thus,  8  m.  5  dm.  G  cm. 
25  mm.  are  added  in  this  manner. 

Added  in  meters:  Added  in  millimeters: 

8  m.         =8  m.  8  m.        =  8000  mm. 

5  dm.       =    .5  m.  5  dm.      =    500  mm. 

6  cm.       =     .06  m.  6  cm.      =       60  mm. 
25  mm.    =     .025  m.  25  mm.  =       25  mm. 


8.585  m.  8585  mm. 

5.  Add  1  m.,  3  dm.,  6  cm.,  3mm.     Add  6.5  m.,  .25  mm.,. 
65  dm. 

6.  The  distance  between  two  towns  is  5  Km.  and  45.V  m. 
After  a  bicyclist  has  traveled  3  Km.  57.5  m.,  how  much  of 
the  distance  remains  to  be  traveled  ? 

7.  The  distance  from  Paris  to  Calais  is  295.32  Km. 
Express  this  distance  approximately  in  miles. 

HAM.    COMPL.    ARITH. — 25 


386 


METRIC   SYSTEM 


8.  How  many  meters  of   ribbon  are  necessary  to  make 
150  badges,  each  25  cm.  in  length? 

9.  The    distance    from     Erie,    Pa.  to    Buffalo,    N.Y.    is 
112.651  Km.     Express  the  distance  approximately  in  miles. 

10.  Reduce  the  decimal  in  the  last  problem  to  meters  and 
lower  denominations. 

11.  The  distance  from  New  York  to  San  Francisco  is  4000 
miles.     Approximate  this  distance  in  kilometers  and  meters. 

METRIC  MEASURES   OF  SURFACE 
Comparison  of  Fundamental  Units  of  Square  Measure 


• 

IS  a. Yd 

ISq.M 

Table  of  Square  Measures 


1  sq.  millimeter  (sq.  mm.) 
1  sq.  centimeter  (sq.  cm.) 
1  sq.  decimeter  (sq.  dm.) 
1  sq.  meter  (sq.  m.) 
1  sq.  decameter  (sq.  Dm.) 
1  sq.  hectometer  (sq.  Hm.) 
1  sq.  kilometer  (sq.  Km.) 


.000001  sq.  meter 
.0001  sq.  meter 
.01  sq.  meter 
1.196  sq.  yd. 
100  sq.  meters 
10000  sq    meters 
1000000  sq.  meters 
(nearly  .4  sq.  mi.) 


In  metric  measure  of  surface  100    times    one  unit   of  any 
denomination  equals  one  unit  of  the  next  higher  denomination. 


MEASURES  OF  VOLUME 


387 


Land  Measure. 

The  standard  unit  used  for  measuring  is  the  are  (ar)  con- 
taining 100  square  meters  =  119.(3  square  yards. 

Table  : 

1  centare  =  1  sq.  meter. 

1  are         =  100  sq.  meters  (nearly  120  square  yards) 

1  hectare  =  10000  sq.  meters  (nearly  2*  acres). 

The  square  meter  is  used  in  measuring  ordinary  surfaces, 
such  as  are  found  in  houses,  lots,  farms,  etc.  ;  the  square 
kilometer  for  measuring  areas  of  countries  and  their  divi- 
sions into  states,  counties,  etc. 


METRIC   MEASURES   OF   VOLUME 
Comparison  of  Fundamental  Units  of  Cubic  Measure 


1  Ctbic  Yard 


1  Cubic  Meter 


Table  of  Solid  or  Cubic  Measures 


1  cu. 

millimeter  (cu.  mm.)  =  .000000001  cu.  meter 

1  cu. 

centimeter  (cu.  cm.)      =  .000001  cu.  meter 

1  cu. 

decimeter  (cu.  dm).    =  .001  cu.  meter 

1  cu. 

meter                              =1  308  cu.  yd. 

In  metric  measure  of  volume  1000  times  <<>"'  unit  of  any  de- 
,  equals  "/<>■  unit  <>f  th<<  next  higher  denomination. 


388  METRIC   SYSTEM 

In  measuring  wood  1  cu.  meter  is  called  a  stere. 
The  cubic  meter  is  the  practical  unit  of  measure  of  vol- 
ume for  all  purposes. 

Written  Work  in  Square  and  Cubic  Measures 

1.  Find  the  number  of  square  meters  in  the  floor  of  your 
schoolroom. 

2.  At  27  cents  per  cubic  meter,  find  the  cost  of  excavating 
a  cellar  10  m.  by  18  m.  by  1|  m. 

3.  How  much  will  it  cost  to  paint  one  side  of  a  tight  board 
fence  25  meters  long  and  3  meters  wide  at  $10  per  square 
decameter  ? 

4.  How  many  square  meters  of  linoleum  will  be  required 
to  cover  the  floor  of  a  hall  8  meters  long  and  3  meters 
wide? 

5.  How  many  steres  are  there  in  a  pile  of  wood  2  meters 
high,  2  meters  wide,  and  6  meters  long? 

METRIC  MEASURES  OF  CAPACITY 
Comparison  of  Fundamental  Units  of  Capacity 


Quart 


MEASURES  (>F   WEIGHT 


:;*!> 


Table   of   Measures   of   Capacity 


1  millimeter  (ml.)  =  .001  of  a  liter 

1  centiliter  (cl.)    =  .01  of  a  liter 

1  deciliter  (dl.)      =  .1  of  a  liter 

1  liter  =  1.0567  liquid  quarts  =  .908  dry  quart. 

1  decaliter  (Dl.)    =  10  liters 

1  hectoliter  (HI.)  =  100  liters  (nearly  2.84  bu.) 


In  metric  measure  of  capacity  10  times  one  unit  of  any  de- 
nomination equals  one  unit  of  the  next  higher  denomination. 
The  liter  is  used  for  liquid  and  dry  measures. 

METRIC   MEASURES  OF   WEIGHT 
Comparison  of  Units  of  Weight 


I  Ounce       I  Gram 


lib. 


I  Kilo 


Table  of  Measures  of  Weight 

1  milligram  (mg.) 

=  .001  of  a  gram 

1  centigram  (eg.) 

=  .01  of  a  gram 

1  decigram  (dg.) 

=  .1  of  a  gram 

1  gram 

=  .03527  of  an  oz  Avoir. 

1  decagram  (Dg.) 

=  10  grams 

1  hectogram  (Hg.) 

=  100  grams 

1  kilogram  (Kg.) 

=  1000  grams  (nearly  2.2  lb.) 

1  myriagram  (Mg.) 

=  1O000  grams 

1  quintal  (Q.) 

=  100000  grams 

1  tonneau  (T.) 

=  1000000  grams  ( nearly  2205  lb.) 

390  METRIC   SYSTEM 

In  the  metric  measure  of  iv eight  10  times  one  unit  of  any  de- 
nomination equals  one  unit  of  the  next  higher  denomination. 

The  gram  is  the  weight  of  1  cubic  centimeter  of  water,  the 
kilogram,  of  1  cubic  decimeter,  and  the  metric  ton,  of  1  cubic 
meter;  the  gram  is  used  by  druggists  and  chemists  ;  the  kilo- 
gram (usually  called  the  kilo)  for  weighing  small  articles; 
and  the  metric  ton  for  large,  heavy  articles. 

Table  of  Metrical  Equivalents 


1  cu. 

mm.  of  water  weighs  1  mg.  and  measures  .001  ml. 

1  cu. 

cm.  of  water  weighs  1  g.  and  measures  1  ml. 

1  cu. 

dm.  of  water  weighs  1  Kg.  and  measures  1  1. 

1  cu. 

m.  of  water  weighs  1  T.  and  measures  1  Kl. 

Written  Work 

Things  sold  in  the  United  States  and  England  by  the  quart 
are  sold  in  countries  using  the  metric  system  by  the  liter. 

1.  Estimate  the  number  of  liters  in  a  tank  2£  m.  long, 
|  m.  in  width,  and  ^  m.  in  depth. 

2.  A  cylindrical  tank  6  m.  in  diameter  and  10  m.  in 
height  is  §  full.  Estimate  the  number  of  liters  it  contains. 
Estimate  the  weight  in  metric  tons. 

3.  A  Paris  milkman  retailed  on  an  average  110  liters  of 
milk  daily  at  25  centimes  a  liter.  Find  the  amount  of  his 
sales  in  our  own  money  for  30  days. 

4.  The  rainfall  in  a  certain  place  in  one  week  was  1  dm. 
Find  the  number  of  liters  that  fell  on  3  hectares  of  land. 

5.  A  horse  eats  4  liters  of  oats  3  times  a  day.  How 
many  hectoliters  does  it  eat  in  60  days  ? 

6.  From  an  olive  orchard,  4.5  Kl.  of  olive  oil  was  put  up 
in  bottles  holding  .5  1.     How  many  bottles  were  used? 


METRICAL    EQUIVALENTS  391 

7.  Find  the  amount  in  United  States  money  from  the  sale 
of  2000  HI.  of  wheat  at  10  francs  per  hectoliter. 

8.  A  German  ice  dealer  retails  blocks  of  ice  .8  m.  in 
length,  .3  m.  in  width,  and  .2  m.  in  thickness.  The  weight 
of  ice  is  .92  that  of  the  same  volume  of  water.  Find  its  cost 
at  3.5  pfennigs  per  kilo.     Find  the  amount  in  our  money. 

9.  Change  a  cubic  meter  of  water  to  liters. 

10.  Find  the  weight  of  a  barrel  of  flour  in  kilos. 

11.  A  stone  8  ft.  by  3  ft.  by  2  ft.  contains  how  many 
cubic  meters  ? 

12.  If  stone  is  2.9  times  as  heavy  as  the  same  volume  of 
water,  find  the  weight  of  the  stone  in  kilo*. 

13.  The  Washington  Monument  is  555  feet  high.  Express 
its  height  in  meters. 

14.  Find  the  cost  of  laying  a  cement  walk  .025  Km.  in 
length  and  1.5.  m.  in  width,  at  $1.70  per  sq.  m. 

15.  Mr.  James  bought  a  tract  of  land  in  the  Philippine 
Islands,  3  Km.  in  length  and  2.5  Km.  in  width,  at  $15.75 
per  hectare.  Find  the  cost  of  inclosing  this  land  with  wire 
fence  at  10^  per  meter. 

16.  A  hallway  is  12  m.  in  length  and  5  m.  in  width.  Esti- 
mate the  number  of  tiles  1  cm.  square  necessary  to  cover  it. 

17.  A  railroad  in  building  a  retaining  wall  used  52000  cu. 
m.  of  stone.  Find  its  weight  in  metric  tons  if  stone  is  2.7 
times  as  heavy  as  the  same  volume  of  water. 

18.  A  city  sewer  is  1.3  Km.  in  length,  1.2  m.  in  width, 
and  averages  3  m.  in  depth.  Estimate  the  number  of  cubic 
meters  of  earth  removed. 

19.  A  certain  kind  of  cloth  costs  90^  per  meter  +  25  % 
ad  valorem  duty.  For  how  much  must  it  be  marked  in 
United  States  mi y  to  gain  25%  on  tlie  yard? 


AGRICULTURAL   PROBLEMS 


FEEDING  STOCK 


Table  of  Digestible  Nutrients  This     table     shows 

the  number  of  pounds 
of  digestible  nutrients 
found  in  100  pounds  of 
each  kind  of  feed  tab- 
ulated. 

A  fair  price  for  these 
nutrients  is  as  follows: 
Protein,  $4  per  cwt. 
Carbohydrates,  40 ^  per 
cwt.  Fat,  $1  per  cwt. 
Find  the  total  value 
of  the  digestible  nutri- 
ents in  1  ton  of  the 
following: 

1.  Timothy  hay.  2. 
Red  clover  hay.  3.  Dry 
corn  fodder.  4.  Corn 
silage.  5.    Wheat 

straw.  6.  Alfalfa  hay. 
7.  Corn,  grain.  8. 
Oats,  grain.  9.  Wheat 
bran.  10.  Oil  meal. 
11.  Oat  straw.  12. 
Cowpeahay.  13.  Corn 
fodder,  green.     14.  Red  clover,  green. 

Protein  is  a  muscle  former,  while  carbohydrates  and  fats  are  fat  formers. 
The  ratio  of  the  muscle  formers  to  the  fat  formers  is  called  the  nutri- 
tive ratio.     A  nutritive  ratio  of  1 :3  is  a  narrow  ratio,  while  one  of  1 :  15 
is  a  wide  ratio. 

A  desirable  nutritive  ratio  for  a  dairy  cow  is  about  1 :5.7;  for  a  work 
horse,  about  1:7;  for  swine,  about  1  :  5.9. 

392 


Feeds 

PRO- 
TEIN 

Carbo- 
hydrates 

Fat 

Corn  fodder,  green  . 

1.1 

12.1 

.4 

Red  clover,  green     . 

3.1 

14.8 

.7 

Alfalfa,  green      .     . 

3.9 

11.2 

.4 

Corn  silage      .     .     . 

1.2 

14.6 

.9 

Corn  fodder,  dry 

2.3 

32.3 

1.1 

Timothy  hay  .     .     . 

2.9 

43.7 

1.4 

Red  clover  hay    .     . 

7.4 

38.1 

1.8 

Alsike  clover  hay     . 

8.1 

11.7 

1.4 

Alfalfa  hay     .     .     . 

10.6 

37.3 

1.4 

Cowpea  hay    .     .     . 

10.8 

38.4 

1.5 

Wheat  straw  .     .     . 

.4 

36.3 

.4 

Oat  straw  .... 

1.2 

38.6 

.8 

Corn,  grain      .     .     . 

7.1 

66.1 

4.8 

Oats,  grain      .     .     . 

9.2 

48.3 

4.2 

Wheat  bran    .     .     . 

12.0 

41.2 

2.9 

Oil  meal     .... 

30.6 

38.7 

2.9 

Cotton-seed  meal     . 

37.0 

16.5 

12.6 

Whole  milk    .     .     . 

3.4 

4.8 

3.7 

Skim  milk       .     .     . 

3.0 

5.0 

.3 

FEEDING    STOCK  393 

Fat,  as  a  food  constituent,  is  regarded  as  2}  times  more  valuable  than 
carbohydrates.  Hence,  the  customary  ride  for  rinding  the  nutritive  ratio 
is  to  add  to  the  carbohydrates  2\  times  the  fat,  and  divide  by  the  protein. 

15.  What  is  the  nutritive  ratio  of  green  corn  fodder? 

Protein,  1.1;  carbohydrates,  12.1;   fat,  .4. 

» 

Tims,  .4  lb.  fat  =  2\  x  .4  lb.  carbohydrates  =  .9  lb.  carbohydrates; 
12.1  lb.  carbohydrates  +  .9  lb.  carbohydrates  =  13  Lb.  carbohydrates; 
13  lb.  -^  1.1  lb.  =  11.8  +.     Hence,  the  nutritive  ratio  is  1  to  11.8  +. 

16.  Find  the  nutritive  ratio  of  a  feed  composed  of  100  lb. 
timothy  hay  and  50  lb.  wheat  bran. 

17.  A  farmer  feeds  his  sheep  100  lb.  of  alfalfa  hay  to 
10  lb.  of  bran.     Find  the  nutritive  ratio. 

18.  An  Ohio  farmer  feeds  his  dairy  cows  100  lb.  red  clover 
hay  to  20  lb.  of  wheat  bran.     Find  the  nutritive  ratio. 

19.  The  best  authorities  suggest  that  a  dairy  cow  weighing 
1000  lb.  and  giving  daily  22  lb.  of  milk  should  be  fed  2.5  lb. 
protein,  13  lb.  carbohydrates,  and  0.5  lb.  fat.  Find  the 
nutritive  ratio  of  this  feed. 

A  balanced  ration  is  a  mixture  of  different  kinds  of  feed  according  to 
a  nutritive  ratio  that  will  produce  the  desired  end  of  the  feeding,  whether 
that  end  be  growth,  fat,  milk,  or  butter. 

20.  A  farmer  mixed  a  balanced  ration  of  3  parts  by 
weight  red  clover  hay  and  1  part  oats  grain.  Find  the 
nutritive  ratio. 

21.  A  feeder  prepared  a  balanced  ration  for  his  hogs  witli 
the  following  parts  by  weight:  1|  parts  corn  grain,  1  part 
oats  grain.      Find  the  nutritive  ratio. 

22.  A  balanced  ration  is  as  follows  :  3  parts  by  weight 
timothy  hay  and  1  part  corn  grain.  Find  the  nutritive 
ratio. 


394  AGRICULTURAL  PROBLEMS 

23.  A  farmer  prepared  a  balanced  ration  consisting  of 
150  lb.  of  alfalfa  hay  and  100  lb.  corn  grain.  Find  the 
nutritive  ratio. 

24.  Find  the  nutritive  ratio  of  a  balanced  ration  consist- 
ing of  200  lb.  corn  silage  and  100  lb.  red  clover  hay. 

25.  What  is  the  nutritive  ratio  of  a  balanced  ration 
that  uses  200  lb.  of  dry  corn  fodder  with  50  lb.  of  wheat 
bran  ? 

26.  A  balanced  ration  for  a  dairy  cow  should  be  about  1 
to  5.7.  Is  the  nutritive  ratio  of  the  following  balanced 
ration  too  wide  or  too  narrow  for  dairy  feeding?  200  lb. 
alsike  clover  hay ;   100  lb.  corn  grain. 

27.  A  balanced  ration  for  work  horses  should  have  a  nutri- 
tive ratio  of  about  1  to  7.  Is  the  nutritive  ratio  of  the  fol- 
lowing ration  too  wide  or  too  narrow  for  work  horses  ? 
200  lb.  timothy  hay  ;  100  lb.  oats  grain. 

28.  A  dairy  man  prepared  a  ration  for  his  cows  consisting 
of  100  lb.  corn  silage,  50  lb.  timothy  hay,  and  100  lb. 
oats  grain.  Find  the  nutritiv-e  ratio.  Is  this  ration  too 
wide  or  too  narrow? 

29.  A  livery  man  feeds  his  horses  on  a  ration  consisting 
of  50  lb.  timothy  hay,  25  lb.  corn  grain,  and  25  lb.  oats 
grain.  Find  the  nutritive  ratio.  Is  this  ratio  too  wide  or 
too  narrow? 

30.  A  stockman  preparing  cattle  for  market  feeds  100  lb. 
red  clover  hay  to  30  lb.  corn  grain,  10  lb.  oats  grain,  and  1 
lb.  oil  meal.     Find  the  nutritive  ratio. 

31.  A  Kansas  farmer  feeds  his  young  cattle  100  lb.  alfalfa 
hay  to  10  lb.  corn  grain  and  2  lb.  cotton  seed  meal.  Find  the 
nutritive  ratio. 


FERTILIZERS 


39:. 


FERTILIZERS 


Poinds  of  Fertilizing  Constit- 
uents in  One  Ton 


This  table  shows  the  num- 
ber of  pounds  of  plant  tood, 
such  as  nitrogen,  phosphoric 
acid,  and  potash  in  one  ton  of 
the  article  named.  All  other 
constituents  necessary  to  plant 
food  can  be  obtained  from  the 
soil,  if  the  water  supply  is  suffi- 
cient and  the  heat  conditions 
proper. 

The  leading  artificial  ferti- 
lizers are  rock  phosphate, 
ground  bones,  ammonia  sul- 
phate, nitrate  of  soda,  animal 
refuse  called  "tankage,"  fish 
scrap,  and  potash  salts,  espe- 
cially the  sulphate  and  the 
muriate  of  potash. 

Lime  is  used  on  land  to  neu- 
tralize the  acidity  of  the  soil. 
Nitrogen  in  fertilizing  material  is  sometimes,  though  not  often,  given 
as  ammonia.     14  lb.  of  nitrogen  correspond  to  17  lb.  of  ammonia. 

Phosphoric  acid  contains  43.6%  phosphorus!  this  constituent  of  ferti- 
lizer is  sometimes,  though  rarely,  given  as  phosphorus.  A  ton  of  timo- 
thy hay  contains  16  lb.  of  phosphoric  acid,  which  is  equivalent  to  7  lb. 
of  phosphorus. 

Potash  contains  83%  potassium.  This  constituent  is  sometimes, 
though  rarely,  given  as  potassium.  A  ton  of  timothy  hay  contains  17 
lb.  of  potash,  which  is  equivalent  to  39  lb.  of  potassium. 

The  value  of  fertilizing  constituents  depends  largely  on  the  forms  in 
which  they  occur.  An  average  value  per  pound  is  15  cents  for  nitrogen. 
3  cents  for  phosphoric  acid,  and  5  cents  for  potash. 

The  composition  of  farm  produce  varies  greatly,  so  that  the  same  kind 
of  crop  may  be  almosl  twice  as  rich  in  certain  constituents  in  some  cases 
as  it  is  in  other  ca-es.  The  table  given  here  is  intended  to  show  the 
am  rage  composition  of  each. 


Materials 

Nitro- 
gen 

I'llos- 
PHORIO 

A.  11. 

P.)T- 

A     11 

Timothy  hay 
Clover  hay  . 
Alfalfa  hay 
Com,  grain 
Corn,  stover 
Bran   .     .     . 
Oat  straw    . 
Milk    .     .     . 
Butter     .     . 
Farm  animals 
Farm  manure 

19 
39 
46 
34 
12 
51 
13 
12 
1.6 
53 
10 

16 

13 

13 

13 

9 

62 

7 

4 

1 

37 

5 

47 
44 
35 

9 

39 
35 

38 
3 
1 
3 

10 

390  AGRICULTURAL   PROBLEMS 

Through  the  growth  of  the  leguminous  plants,  such  as  clover,  alfalfa, 
beans,  peas,  etc.,  it  is  estimated  that  the  farmer  may  obtain  nitrogen 
from  the  air  at  a  cost  of  about  2|  f  per  pound. 

1.  How  much  nitrogen  is  required  to  produce  each  of  the 
following  :  6  tons  clover  hay  ?  3000  lb.  corn  grain  ?  5500 
lb.  timothy  hay  ?     4  tons  alfalfa  ? 

2.  How  much  potash  did  a  farmer  sell  in  1500  lb.  of  but- 
ter ?  in  760  lb.  milk  ?  in  5  steers  averaging  1450  lb.  each  ? 

3.  A  farmer  cut  on  an  average  3  tons  per  acre  of  clover 
hay  from  a  5  acre  field.  How  many  tons  of  manure  are 
required  for  the  field  to  supply  the  phosphoric  acid  in  the 
hay? 

4.  A  farmer  sold  50  tons  of  timothy  hay  in  one  season. 
How  many  tons  of  farm  manure  will  balance  the  loss  in 
potash  ? 

5.  When  nitrogen  is  worth  16^  per  pound,  phosphoric 
acid  5^,  and  potash  0^,  find  the  fertilizing  value  of  5  tons 
of  farm  manure. 

6.  A  commercial  fertilizer  when  analyzed  was  found  to 
contain  by  weight  3.4%  nitrogen,  6.6%  phosphoric  acid, 
and  9%  potash.  Find  its  value  per  ton,  when  nitrogen 
is  worth  15^  per  pound,  phosphoric  acid  3^  per  pound  and 
potash  5^  per  pound. 

7.  The  analysis  of  a  certain  brand  of  bone  meal  showed 
the  following:  1.6%  nitrogen,  and  27.9%  phosphoric  acid. 
What  is  its  value  per  ton  at  15  ^  per  pound  for  nitrogen  and 
Z\$  per  pound  for  phosphoric  acid. 

8.  A  farmer  sold  500  bu.  of  corn  grain  (shelled  corn  56 
lb.  to  the  bushel)  from  a  certain  field.  How  many  tons  of 
farm  manure  will  supply  the  field  with  the  phosphoric  acid 
removed  by  the  corn  grain  ? 


sn;.\Y!\<;  plants  39' 


SPRAYING   PLANTS 


The  Bordeaux  mixture  used  for  killing  fun- us  growths  — such  as  Mack 
rot  and  scab  of  apples,  black  rot  and  mildew  of  grapes,  brown  rot  of 
plums  and  cherries,  etc.  —  was  first  discovered  in  Bordeaux.  France.  To 
make  a  solution  for  spraying:  first,  dissolve  4  pounds  of  copper  sulphate, 
(blue  vitrol)  in  25  gallons  of  water;  second,  dissolve  4  pounds  of  freshly 
slaked  stone  lime  in  25  gallons  of  water  until  it  forms  a  milk  of  lime; 
third,  pour  the  two  solutions  together  and  they  are  ready  for  use.  The 
solution  should  be  applied  to  the  fruit  while  small.  In  this  way  a  coak 
ing  is  formed  over  the  fruit  through  which  the  fungus  cannot  grow. 

Note.  — In  all  directions  for  spraying,  50  gallons  are  considered  a  barrel. 

1.  For  a  vineyard  of  25  acres  of  grapes  suffering  from 
black  rot  of  the  fruit,  how  many  pounds  of  sulphate  of 
copper  and  lime  are  necessary,  if  100  gallons  of  Bordeaux 
mixture  will  spray  §  of  an  acre  ? 

2.  If  sulphate  of  copper  can  be  boughtat  6/  per  pound, 
and  stone  lime  at  \$  per  pound,  what  is  the  cost  of  mate- 
rials for  500  gallons  of  Bordeaux  mixture  ? 

3.  If  a  man  with  a  team  of  horses  at  $3.50  per  day,  using 
a  geared  sprayer,  can  spray  3  acres  of  vineyard  in  a  day,  and 
Bordeaux  mixture  costs  27/  per  barrel,  using  10  barrels  per 
day,  what  is  the  cost  of  spraying  30  acres  of  grapes  ? 

4.  600  bushels  of  apples  from  40  trees  without  spraying 
for  fungus  growth  were  sold  as  follows :  100  bu.  of  perfect 
fruit  at  81  per  bushel,  and  500  bu.  of  scabby  and  wormy 
fruit  at  30/  per  bushel.  If  spraying  at  15/  per  tree  re- 
versed the  quantities  of  perfect  and  imperfect  fruit,  what 
would  be  gained  by  spraying  ? 

5.  The  estimated  value  of  a  crop  of  grapes  is  $400  per 
acre.  Thorough  spraying  costs*  $6  per  acre.  If  without 
spraying,  fungus  diseases  destroy  30  %  of  the  crop,  what  is 
the  net  value  of  the  spraying  of  10  acres  ? 

HAM.   SCH.   ARITH.  — 21 


398  AGRICULTURAL   PROBLEMS 

6.  The  average  yield  from  4  acres  of  sprayed  grapes  was 
4770  lb.  per  acre,  and  the  yield  from  unsprayed  grapes  was 
3108  lb.  The  grapes  were  sold  for  2±^  per  pound.  The 
cost  of  spraying  was  $8.60  per  acre.  What  was  the  net 
gain  on  the  4  acres  as  a  result  of  spraying? 

A  Paris  green  solution  is  used  for  killing  chewing  insects  that  destroy 
the  plants  by  eating  the  leaves;  and  for  destroying  the  codling  moth  to 
prevent  wormy  fruit.  A  solution  for  this  purpose  is  made  by  mixing  i 
ounces  of  Paris  green  with  50  gallons  of  water,  a  sufficient  amount  to 
spray  20  apple  trees.  When  fungus  diseases  are  to  be  controlled  also,  the 
Paris  green  is  added  to  Bordeaux  mixture. 

7.  What  is  the  cost  of  materials  to  spray  an  apple  orchard 
of  250  trees,  for  the  apple  worm,  with  Paris  green  at  32^  per 
pound,  using  a  barrel  of  the  solution  to  20  trees  ? 

8.  Mr.  Wagner  sprayed  8|  acres  of  potatoes  4  times  with 
Bordeaux  mixture  containing  Paris  green  to  control  blight, 
rot,  and  insects.  His  expense  account  was  as  follows:  183 
lb.  copper  sulphate  at  8^;  204  lb.  lime  at  #1.15  per  hun- 
dred; 10  lb.  Paris  green  at  35  ^;  48  hr.  labor  for  a  man  at 
20^;  40  hr.  labor  for  team  at  15  ^;  wear  of  sprayer,  $1.50. 
What  was  the  cost  of  spraying  per  application  per  acre  ? 

9.  The  8|  acres  mentioned  above  yielded  1567.5  bu.  pota- 
toes. A  portion  of  the  same  field  that  was  left  unsprayed 
yielded  at  the  rate  of  156  bu.  per  acre.  Mr.  Wagner  sold 
his  crop  for  55^  per  bushel.  What  was  his  net  profit  per 
acre  resulting  from  spraying  ? 

10.  Mr.  Gould  sprayed  an  orchard  of  240  trees  five  times 
during  the  season,  using  altogether  3013  gal.  Bordeaux 
mixture  containing  Paris  green.  The  cost  of  materials  was: 
Copper  sulphate,  256  lb.  fit  8^;  lime,  347  lb.  at  \t\  Paris 
green,  \b\  lb.  at  35^;  and  the  cost  of  applying  was  labor, 
3  men,  \\  days  at  $1.50;  1  team,4|  days  at  $1.50;  wear  on 


SPRAYING    PLANTS  399 

spray  machinery,  $5.  Determine  the  cosl  of  materials  and 
the  cost  of  applying  per  gallon  and  also  per  tree,  including 
wear  on  machinery. 

11.  Thirty-four  apple  trees  sprayed  to  control  scab  and 
codling  moth  yielded  90  bu.  merchantable  fruit  and  32  bu. 
culls  and  windfalls.  In  the  same  orchard  21  unsprayed  trees 
yielded  11  bu.  merchantable  fruit  and  40  bu.  culls  and  wind- 
falls. The  merchantable  apples  were  sold  for  67^  per  bushel 
and  the  culls  and  windfalls  for  22^  per  bushel.  The  cost  of 
spraying  was  25^  per  tree.  What  was  the  net  gain  from 
spraying  per  tree? 

Kerosene  Emulsion  is  used  to  kill  insects  that  suck  the  juices  of  plants. 
A  solution  for  this  purpose  is  made  as  follows  :  first,  dissolve  2  ounces  of 
soap  in  one  quart  of  water  by  heating  until  the  soap  is  dissolved ;  second, 
add  two  quarts  of  kerosene  oil  and  stir  for  five  minutes;  third,  add  to 
this  mixture  17  quarts  of  water  to  make  5  gallons  of  a  10%  mixture. 
After  thorough  stirring,  it  is  ready  for  use. 

12.  What  would  be  the  cost,  at  12^  per  gallon,  for 
enough  kerosene  to  make  500  gallons  of  a  10  %  kerosene 
emulsion  that  might  be  used  on  plants  in  leaf ?  To  make 
128  gallons  of  an  8  %  emulsion  ? 

13.  A  farmer  has  b\  A.  of  cabbage.  He  estimates  that 
the  yield  will  be  6500  heads  per  acre,  and  that  the  selling 
price  will  be  1\t  per  head.  Cabbage  lice  threaten  a  loss  of 
10%.  If  by  applying  kerosene  emulsion  at  a  cost  for  mate- 
rials and  labor  of  $7.25  per  acre,  the  loss  can  be  reduced  to  2  %, 
what  will  be  the  gain  from  applying  the  treatment  to  the  b\  A.? 

14.  A  nurseryman  used  10%  kerosene  emulsion  to  kill 
plant  lice  on  his  roses  and  young  fruit  stock.  His  expendi- 
ture for  kerosene  was  $4.50.  If  kerosene  was  15^  per  gal- 
lon, how  many  gallons  of  the  10%  mixture  did  he  use? 
How  many  pounds  of  suap  were  used  in  making  it  ? 


400  AGRICULTURAL   PROBLEMS 

The  San  Jose"  scale  is  a  very  small  insect  not  larger  than  the  head  of 
a  pin.  It  injures  the  tree  by  sucking  the  juice  of  the  bark.  A  lime- 
sulphur  solution  for  killing  the  insect  is  made  as  follows:  hist,  dissolve 
20  pounds  of  freshly  slaked  lime  and  15  pounds  of  sulphur  in  12  gallons 
of  water,  boiling  the  mixture  1  hour;  second,  add  to  this  enough  water 
to  make  50  gallons  of  spraying  mixture.  This  forms  a  hard  covering 
over  the  tree,  thereby  preventing  the  scale  insect  from  doing  further 
harm. 

15.  If  sulphur  is  worth  3^  per  pound  and  lime  is  worth 
\t  per  pound,  and  the  labor  of  making  lime-sulphur  solution 
is  worth  15^  per  barrel,  what  will  be  the  cost  of  making 
enough  solution  to  spray  an  orchard  of  252  peach  trees,  25 
gallons  being  sufficient  for  9  trees? 

16.  In  the  above  mentioned  orchard,  the  cost  of  applying 
is  85  %  of  the  cost  of  solution.  How  much  does  it  cost  per 
tree  to  spray  the  orchard?  If  one  application  per  year  for 
ten  years  prolongs  the  life  of  each  tree  four  years  and  the 
average  annual  yield  of  fruit  is  worth  $1.25,  what  is  the  net 
gain  per  tree  due  to  prolonged  life? 

17.  A  lime-sulphur  solution  costs  75^  per  barrel  to  make, 
and  a  soluble  oil  preparation  for  killing  scale  insects  costs 
$1.25  per  barrel.  A  barrel  of  the  former  will  cover  18  trees 
and  a  barrel  of  the  latter  15  trees.  What  would  be  the  sav- 
ing from  using  a  lime-sulphur  solution  on  a  ten  acre  orchard 
of  pear  trees  set  140  to  the  acre,  the  cost  of  applying  being 
equal  and  the  solutions  being  equally  effective  insecticides? 

18.  The  market  value  of  a  crop  of  peaches  is  $225  per 
acre.  The  total  cost  of  production,  including  interest  on  in- 
vestment, cost  of  marketing,  etc.,  is  $175  per  acre.  What 
would  be  the  per  cent  of  loss  on  the  market  value  from  fun- 
gus diseases  and  insect  injuries,  if  the  market  value  is  so 
reduced  as  to  equal  the  cost  of  production  ? 


TEST   PROBLEMS 

1.  J.  P.  Black  &  Co.'s  bank  account  is  overdrawn  $182.50. 
They  place  to  their  credit  a  90-day  note  for  11500  with  in- 
terest at  6%,  discounted  30  days  after  date.  They  then 
deposit  $84.30  and  check  on  their  account  to  the  extent  of 
$341.65.  Find  their  balance  in  bank,  if  the  custom  of  this 
bank  in  discounting  is  to  count  both  the  day  of  maturity  and 
the  day  of  discount. 

2.  A  cow  is  tied  in  the  corner  of  a  square  field  by  a  rope 
2  rods  lonsr.  Find  the  extent  of  the  surface  over  which  it 
can  graze. 

3.  A  cold  air  register  is  18  in.  by  30  in.  What  are  the 
dimensions  of  a  similar  register  to  let  in  double  the  volume 
of  cold  air? 

4.  A  clothier  sold  a  suit  marked  $24,  at  10%  off  for  cash, 
making  a  profit  of  20  %.      How  much  did  the  suit  cost? 

5.  There  are  50  persons  in  a  schoolroom  36  ft.  long,  30  ft. 
wide,  and  15  ft.  high.  How  many  cubic  feet  of  air  space  are 
there  for  each  person?  The  law  fixes  the  minimum  of  fresh 
air  at  30  cubic  feet  per  minute  per  person.  How  frequently 
must  the  room  be  filled  with  air  to  meet  this  requirement  ? 

6.  A  municipality  paved  a  street  48  ft.  from  curb  to  curb 
at  $1.60  per  square  yard,  under  an  ordinance  that  assessed 
property  holders  abutting  on  the  street  |  of  the  cost- 
Mr.  James  owns  two  lots  each  25  ft.  wide  fronting  on  the 
street.  He  puts  in  a  curb  at  75^  per  linear  foot  and  a  side- 
walk 12  ft.  wide  at  $1.80  per  square  yard.  How  much  is 
his  bill  for  the  improvements? 

lot 


402  TEST   PROBLEMS 

7.  A  conical  glass  is  4  inches  in  diameter  and  6  inches 
high.  How  often  can  it  be  filled  from  a  cylindrical  vessel 
4  inches  in  diameter  and  12  inches  high  ? 

8.  An  article  was  sold  at  2") oj0  advance  on  the  cost.  The 
proceeds  were  invested  in  a  second  purchase  which  was  after- 
wards sold  for  $240.  The  latter  sale  was  at  a  loss  of  20  c/0. 
Find  the  selling  price  of  the  first  article. 

9.  It  cost  1280  to  fence  a  field  80  rods  long  and  60  rods 
wide.  How  much  less  will  it  cost  to  fence  a  square  field  of 
equal  area  with  the  same  kind  of  fence? 

10.  How  much  will  it  cost  to  bronze  a  globe  12  inches  in 
diameter  with  gold  leaf  at  5^  per  square  inch  ? 

11.  The  diameter  and  altitude  of  a  cone,  the  diameter  of 
the  base  and  the  altitude  of  a  cylinder,  and  the  diameter  of 
a  globe  are  each  3  ft.     Find  the  volume  of  each. 

12.  A  town  assessed  at  $2,450,000  must  raise  a  tax  of 
$7766.25.  The  poll  tax  is  $825.  Find  the  tax  rate,  if  the 
collector  is  allowed  5  %  for  collecting. 

13.  When  the  Florida  collided  with  the  Republic  off  the 
coast  of  Massachusetts,  the  wireless  message  summoned  the 
Baltic  to  the  wreck  from  a  point  62  miles  north  and  84  miles 
east.     What  was  the  distance  in  a  direct  line  ? 

14.  A  merchant  sold  20  lb.  more  than  l  of  his  butter. 
He  then  reduced  the  price  b$  per  pound,  thereby  reducing 
his  profit  $  2.     How  many  pounds  had  he  at  first  ? 

15.  Mr.  Adams  sold  50  %  of  his  stock  at  20  %  gain,  and 
80%  of  the  remainder  at  25%  gain.  What  was  his  total 
gain,  if  the  stock  unsold  cost  $1000? 


TEST    PROBLEMS  403 

16.  A  cow  and  a  horse  cost  8190,  and  $  the  cost  of  the 
cow  plus  $12  equal  -^  the  cost  of  the  horse.  Find  the  cost 
of  each. 

17.  A  piece  of  steel  in  the  form  of  ;i  cylinder  is  4  ft.  long 
and  2  inches  in  diameter.  How  long  is  it  when  rolled  into  a 
bar  1  inch  square  ? 

18.  A  rectangular  field  that  contains  40  acres  is  four  times 
as  long  as  it  is  wide.     Find  its  dimensions. 

19.  A  man  bought  a  tenement  containing  8  apartments  for 
§35,000.  His  taxes,  repairs,  and  insurance  cost  him  81157 
annually.  He  rented  4  suites  at  840  per  month,  2  suites 
at  §35  per  month,  and  2  suites  at  §28  per  month.  What 
per  cent  did  he  realize  on  his  investment  ? 

20.  If  a  piano  is  marked  80  %  above  cost,  what  per  cent 
discount  can  be  allowed  from  the  marked  price  to  realize 
20  %  profit  ? 

21.  The  edge  of  a  cube  is  10  inches.     Find  its  diagonal. 

22.  Find  the  shortest  distance  on  the  surface  of  the  cube 
mentioned  in  Ex.  21  between  two  diagonally  opposite  corners. 

23.  A  rectangular  box  is  8  ft.  long,  6  ft.  wide,  and  4  ft.  high. 
Find  the  dimensions  of  a  similar  box  whose  length  is  12  ft. 

24.  What  is  the  ratio  of  the  volume  of  the  two  boxes 
mentioned  in  Ex.  23  ? 

25.  Find  the  duty  in  U.S.  money  on  an  invoice  of  leather 
from  Paris,  if  the  leather  costs  12,350  francs  and  the  duty  is 
35%  ad  valorem. 

26.  Rose  Adhorn  and  Co.  imported  10  cases  of  woolen 
goods  from  England  of  385  pounds  each,  invoiced  at  £  408 
per  case.  Find  the  total  duty  at  40^  per  pound  and  60  <f0 
ad   valorem. 


404  TEST    PROBLEMS 

27.  A  merchant  sold  goods  for  $1242;  one  half  he  sold 
at  an  advance  of  20  %  on  the  cost,  three  tenths  at  an  advance 
of  16|  %,  and  the  remainder  at  cost.  How  much  did  he  pay 
for  the  goods  ? 

28.  Two  successive  trade  discounts  of  20  %  and  10  %  re- 
duced a  bill  $560.     What  was  the  original  bill  ? 

29.  I  sold  my  horse  for  $180  and  took  in  payment  a  90-day 
note  bearing  interest  at  5%,  dated  Feb.  1,  1909.  On  April  5, 
I  had  the  note  discounted  at  the  bank  at  6  %.  What  were 
the  proceeds  of  the  note  ? 

30.  I  asked  for  a  grain  binder  40  °]o  more  than  it  cost.  I 
accepted  ^  of  what  I  asked,  and  gained  $  15.  How  much  did 
I  ask? 

31.  I  have  a  rectangular  field,  the  perimeter  of  which  is 
240  rods.  It  is  twice  as  long  as  it  is  wide.  How  many  acres 
does  it  contain  ? 

32.  A,  B,  &  C  have  1400  acres  of  land.  \  of  A's  share 
is  equal  to  \  of  B's,  and  |  of  B's  share  is  equal  to  |  of  C's. 
How  many  acres  has  each  ? 

33.  Mr.  Fair  bought  five  $1000,  5%  San  Francisco  water 
bonds,  due  in  6  years,  at  104,  brokerage  \$o-  He  sold  the 
bonds  one  }rear  before  they  were  due  at  102,  brokerage  \  %. 
Find  his  average  annual  rate  of  income. 

34.  A  90-day  note  for  $  640,  without  interest,  is  discounted 
at  the  bank  at  6  %  on  the  day  of  issue.  Find  the  proceeds 
of  the  note.  What  would  be  the  proceeds,  if  the  note  read 
"  with  interest "  ? 

35.  I  buy  furniture  listed  at  $4400,  getting  trade  discounts 
of  20%,  10  %,  and  5  %  ;  I  sell  at  40  %  above  cost,  taking  a 
120 -day  note  in  payment  without  interest.  I  have  the  note 
discounted  at  6  <f0  on  the  day  of  sale.     How  much  do  I  gain  ? 


TEST    PROBLEMS  105 

36.  A  solid  bar  of  silver  weighs  6|  lb.  avoirdupois.  Esti- 
mate its  weight  by  Troy,  and  its  value  at  53^  per  ounce. 

37.  A  steel  ingot  is  16  in.  square  and  8  ft.  long.  What 
Lenerth  of  steel  bar  will  it  make  4  in.  thick  and  6  in.  wide? 

38.  Find  the  cost  at  27 ^  per  load,  to  excavate  the  ground 
for  a  cellar  2-1  ft.  wide,  and  42  ft.  long,  the  ground  being 
excavated  to  a  depth  of  7^  ft.  at  one  end  and  2  ft.  4  iu.  at 
the  other  end. 

39.  Mr.  Samuels  bought  eight  $1000,  4%,  ten-year  bonds 
when  issued,  interest  payable  semiannually,  at  97|-,  broker- 
age |%.  After  keeping  the  bonds  3|  years,  he  sold  them 
at  110],  brokerage  \  %,  and  loaned  the  money  at  6%  interest 
for  2^  years.  Find  his  average  annual  income  on  the  original 
investment  for  the  6  years. 

40.  A  boy  climbs  a  flag  pole  to  the  height  of  40  feet.  An- 
other boy  is  standing  on  the  ground  120  feet  from  the  foot  of 
the  flag  pole.  If  the  second  boy  is  165  feet  from  a  ball  on 
the  top  of  the  pole,  how  far  is  the  first  boy  from  the  ball  ? 

41.  The  product  of  two  equal  factors  multiplied  by  a  third 
factor,  7,  and  that  product  by  a  fourth  factor,  8,  is  35,000. 
What  are  the  equal  factors? 

42.  Mr.  Adams  buys  two  *  1000,  5-year,  5  %  bonds,  inter- 
est payable  semiannually,  that  have  3^-  years  to  run.  tor 
*1020  each,  brokerage  \°/o-  Find  his  average  annual  in- 
come, if  he  keeps  the  bonds  until  due  ? 

43.  Mr.  Brown  sells  five  ^1000,  10-year,  4%  bonds,  inter- 
est payable  semiannually,  that  have  4|  years  to  run,  at  90^ 
on  the  dollar,  brokerage  \%.  Find  the  buyer's  average  rate 
of  income,  if  the  bonds  are  redeemed  when  due  without 
brokerage. 


GENERAL  REVIEW 

Oral  Problems 

1.  A  boy  buys  oranges  at  25  cents  per  dozen  and  retails 
them  at  3  for  10  cents.     Find  his  gain  per  cent. 

2.  Mr.  Henderson  was  earning  $3.50  per  day  of  10  hours. 
His  wages  were  reduced  20  %  •  Find  the  rate  of  wages  per 
hour  he  then  earned  and  his  daily  wages. 

3.  A  man  purchased  4  %  bonds  at  par.  How  many  dol- 
lars' worth  did  he  purchase  if  his  income  from  the  bonds 
was  $1200  per  year  ? 

4.  A  merchant  buys  potatoes  at  60  cents  per  bushel  and 
retails  them  at  30  cents  per  peck.     Find  his  gain  per  cent. 

5.  A  can  do  |  of  a  piece  of  work  in  10  hours  and  B  can 
do  |  of  it  in  9  hours.  In  how  many  hours  working  together 
can  they  do  the  work  ? 

6.  If  I  sell  |  of  an  article  for  |  of  the  cost,  what  per 
cent  do  I  lose  ? 

7.  A  book  dealer's  selling  price  is  25  %  above  cost.  A 
special  discount  of  10%  is  allowed  to  teachers.  A  teacher 
pays  him  $14.85  for  books.     Find  the  dealer's  profit. 

8.  A  merchant  buys  goods  at  a  discount  of  20  %,  5  %  off, 
and  sells  them  at  the  list  price.     Find  the  per  cent  of  profit. 

9.  Read  as  per  cents :  ^,  £,  |,  1£,  |,  -^g,  -^,  .16|,  .05,  .06|, 

.37£,  .40,  .25. 

406 


GENERAL  REVIEW  407 

10.  M  and  N  have  a  profit  of  $1700  in  business,  §  of 
iM's  capital  equals  |  of  N's  capital.  How  should  the  profit 
be  divided  ? 

11.  A  man  sold  \  of  his  farm  to  B,  |  of  the  remainder  to 
C,  and  the  remaining  60  acres  to  D.  How  many  acres  were 
in  the  farm  at  first  ? 

12.  A  coal  merchant  pays  $2  per  ton  for  coal.  The 
freight  and  delivery  cost  him  50^  per  ton.  If  he  retails 
the  coal  at  $3  per  ton,  find  his  per  cent  of  profit  on  the 
entire  cost  of  the  coal. 

13.  Wishing  to  find  whether  a  corner  was  square,  a  man 
measured  8  feet  along  one  side  from  the  corner  and  6  feet 
along  the  other  side  from  the  corner.  What  should  be  the 
distance  between  the  ends  of  the  lines  if  the  corner  is  square  ? 

14.  Explain  why,  when  it  is  12  o'clock  M.  at  Washington, 
it  is  approximately  9  o'clock  a.m.  at  San  Francisco  and  5 
o'clock  p.m.  at  London  (standard  time). 

15.  A  commission  house  received  a  consignment  of  peaches 
at  10%  and  retailed  them  at  $1.50  per  bushel  crate.  If  the 
commission  was  $45,  how  many  bushel  crates  were  sold  ? 

16.  After  depositing  f  of  his  month's  salary,  a  man  pays 
with  the  remainder  bills  of  $8,  $12,  and  $25,  and  has  $30 
left.     Find  his  monthly  salary. 

17.  30%,  10%,  5%  off  is  equivalent  to  what  single  com- 
mercial discount  ? 

18.  27  cents  is  |  %  of  how  many  dollars  ? 

19.  A  retailer  bought  pencil  tablets  at  $2.40  per  hundred 
and  sold  them  at  5  cents  each.     Find  the  gain  per  cent. 

20.  An  automobile  was  sold  for  $1200  at  a  loss  of  25%. 
What  would  have  been  the  loss  per  cent  if  it  had  been  sold 
for  $1500  ? 


408  GENERAL   REVIEW 

21.  The  surface  of  a  cube  is  96  square  inches.  Find  its 
volume. 

22.  A  house  and  lot  cost  §6000.  It  rents  for  8360  a  year. 
The  taxes  average  1%,  insurance  |%,  and  repairs  $30. 
What  is  the  rate  per  cent  of  net  income  ? 

23.  A,  B,  and  C  gain  $2100  in  business.  A's  share  of  the 
profits  is  |  of  B's,  and  C's  share  of  the  profits  is  equal  to  A's 
and  B's  together.     Find  the  profits  of  each. 

24.  $2900  is  divided  between  two  partners  in  the  ratio  of 
1|  to  1|.     Find  each  one's  share. 

25.  A  withdraws  |  of  his  deposit  in  a  bank.  He  then  de- 
posits ^  as  much  as  he  has  drawn  out,  and  still  has  $2500  in 
the  bank.     Find  the  amount  in  the  bank  at  first. 

26.  A  block  of  business  houses  was  insured  for  -|  of  its 
value  at  3  %.  If  the  premium  was  $600,  what  was  the  value 
of  the  block  ? 

Written  Work 

27.  Simplify:    a.  41  *  ^  ~  5*  J.  L!i±l 

4  of  1  of  A  i  nf   5    i     7 

3   Vl    4  Ui    5  4  U1    6   +   8 

28.  A  commission  of  $43.47  was  charged  for  selling  $1242 
worth  of  goods.     What  was  the  rate  of  commission  ? 

29.  How  many  yards  are  there  in  3.1  mi.?   in  7.9  Km.? 

30.  What  are  the  proceeds  of  a  note  for  $400,  when  dis- 
counted for  95  days  at  6  %  ? 

31.  A  lawyer's  commission  for  collecting  a  bill,  at  5  %, 
was  $125.50.     Find  the  amount  of  the  bill. 

32.  The  square  of  a  number  is  1024.     What  is  its  cube  ? 

M     Q.      v.*  4  x    1  x  25  ,    /37!       2A\      U 

33.  kMmplif  v  :    a.  5 6.      — a.  _= — a     x  _2. 

"  fx  11x10  U|        2iJ      21 


GENERAL    REVIEW  109 

34  A  bankrupt's  liabilities  are  #15000  and  his  assets 
#'.•000.  How  much  does  a  creditor  receive  whose  claim  is 
$6000,  no  allowance  being  made  for  court  costs? 

35.  How  many  cakes  of  soap  4  in.  long,  2  in.  wide,  and  I.1, 
in.  thick  can  be  packed  in  a  box  2  ft.  long,  1  ft.  wide,  and 
1  ft.  high  ? 

36.  Write  in  figures  the  number  eleven  million,  eleven 
thousand  eleven,  and  eleven  millionths. 

37.  What  is  the  square  root  of  14^  ? 

38.  Find  the  sum  of  the  quotients : 

3-3  3  -  .03  300  -=-  30 

3  -*-  .3  .003  -j-  3  30  --  300 

.03  -=-  3  30  -  .03  .03  -*-  30 

39.  In  a  town  83500  was  raised  from  a  tax  of  14  mills. 
What  was  the  assessed  valuation  of  the  property? 

40.  The  perimeter  of  a  square  field  is  320  rods.  How 
many  acres  does  it  contain  ? 

41.  Reduce  to  decimals:   f,  |,  ^  T9g,  f,  ^. 

42.  A  man  borrowed  I860  September  1,  1903,  and  paid 
the  note  Jan.  16,  1900,  with  interest  at  7%.  How  much 
was  paid  at  settlement  ? 

43.  Find  the  omitted  term  in  each: 

5:     8  =  15:  ()  J:f       =0  =  f 

():12=    5:4  1£  :  (  )  =    3|  :  4£ 

44.  I  pay  $36  for  insuring  my  house  at  |  %.  For  how 
much  is  the  house  insured  ? 

45.  Find  the  exact  interest  of  $180  from  April  1,  1904  to 
August  25,  1904,  at  6%. 

46.  The  assessed  valuation  of  a  town  is  #875000.  What 
rate  must  be  levied  to  raise  $10937.50? 


410  GENERAL   REVIEW 

47.  A  60-day  note  for  $1000  is  discounted  at  a  bank  at 
8  %  on  the  date  of  issue.     Find  the  proceeds. 

48.  A  speculator  buys  a  tract  of  land  4^  miles  square. 
How  many  sections  does  it  contain?  How  much  will  it  cost 
to  put  a  fence  around  it  at  $0.50  per  rod  ? 

49.  Find  the  cost  of  the  following  bill  of  lumber: 

30  pieces  30'  x  6"  x  12"  at  $30  per  M. 

60  pieces  24'  x  6"  x  8"  at  $24  per  M. 
120  pieces  18'  x  4"  x  6"  at  $20  per  M. 
150  pieces  16'  x  3"  x  4"    at  $18  per  M. 

50.  A  commission  merchant  sold  2240  pounds  of  butter  at 
24^  a  pound.  His  commission  for  selling  was  5%  and  he 
paid  freight  charges  amounting  to  $5.72.  How  much  did  he 
remit  to  the  shipper  ? 

51.  A  barn  valued  at  $1800  is  insured  for  |  of  its  value, 
at  1 1  %  for  a  term  of  3  years.  Find  the  average  annual  cost 
of  insurance. 

52.  $200  was  borrowed  at  5%  on  Oct.  1,  1904.  When  it 
was  paid,  it  amounted  to  $217.50.  On  what  date  was  it 
paid  ? 

53.  Two  successive  discounts  of  20%  and  15%  reduce 
a  bill  to  $306.     How  much  was  the  original  bill  ? 

54.  From  a  piece  of  land  45  rods  square,  I  sold  145  square 
rods.     What  is  the  value  of  the  remainder,  at  $60  an  acre  ? 

55.  Simplify:     a.      »       '  _  ^         *     b.  ^f-     8         'J 

-t  +    8         X 3   +   12  '  2    X  8¥   X  TT 

56.  A  note  for  $320,  dated  June  1,  1902,  falls  due  Septem- 
ber 16,  1904.  What  amount  will  pay  the  note  if  it  draws 
4|%  simple  interest? 

57.  What  is  the  tax  on  property  assessed  for  $12480  at 
$13.50  a  thousand? 


GENERAL    REVIEW  -111 

58.  A  broker's  purchase  at  105,  with  his  brokerage  at  \<?0, 
was  $6307.50.     How  many  shares  were  bought? 

59.  In  what  time  will  any  principal  double  itself  at  5  %  ? 
at  6  %  ?   at  8  %  ? 

60.  A  street  40  rods  long  and  40  feet  wide  is  to  be  graded 
down  on  an  average  1|  feet.  How  much  will  the  excavating 
cost  at  27  f  a  cubic  yard  ? 

61.  A  coal  dealer  bought  200  tons  of  coal  at  $3.50  per 
long  ton  and  sold  it  at  $4.20  per  short  ton.     Find  the  gain. 

62.  A  wholesale  merchant  imports  30000  yards  of  Brus- 
sels carpet,  27  inches  wide,  purchased  in  Belgium  at  40  ^  per 
yard.  The  duty  is  18  ^  per  yard  and  40  c/0  ad  valorem. 
Find  the  wholesale  price  in  the  United  States,  if  a  profit  of 
25  <f0  on  the  yard  is  made. 

63.  I  invested  $5000  in  bank  stock  at  156  and  sold  it  at 
167,  brokerage  \°/o  in  each  case.     Find  the  gain. 

64.  The  specific  gravity  of  oak  is  .934.  Find  the  weight 
of  an  oak  sill  24  ft.  x  1  ft.  x  1  ft. 

65.  The  residence  of  Mr.  Daniels  valued  at  $  8000  was  in- 
sured for  3  years  at  90  cents  per  $100  on  80%  of  its 
valuation.     How  much  was  the  average  annual  premium  ? 

66.  A  man  45  years  old  takes  out  a  $  5000  life  insurance 
policy  payable  in  20  years.  If  he  pays  an  annual  premium 
of  $36.87  on  the  $1000,  and  lives  till  the  policy  falls  due, 
how  much  will  his  insurance  cost  him,  estimating  that  he 
gets  back  in  dividends  an  average  of  20  %  of  the  premiums 
paid? 

67.  A  train  running  30  miles  an  hour  is  54  minutes  in 
going  from  one  city  to  another.  If  it  makes  3  stops  of  4 
minutes  each,  how  far  apart  are  the  cities  ? 


412  GENERAL   REVIEW 

68.  A  square  field  contains  10  acres.  How  much  longer 
is  its  diagonal  than  its  side  ? 

69.  A  man  desires  to  realize  6  %  on  his  investment.  How 
much  should  he  pay  for  borough  bonds  bearing  4|  %  interest? 

70.  In  an  examination  150  questions  were  asked  each  of 
5  members  of  a  class.  The  first  answered  140,  the  second 
135,  the  third  and  fourth  120  each,  and  the  fifth  110.  Find 
the  average  per  cent  of  the  class. 

71.  A  farm  roller  8  ft.  long  and  2|  ft.  in  diameter  will 
pass  over  how  much  surface  in  100  revolutions  ? 

72.  The  floor  of  a  room  is  16  ft.  x  131  ft.  Find  the  cost 
of  carpeting  it  with  carpet  f  of  a  yard  wide,  laid  lengthwise 
and  costing  $1.20  a  yard,  allowing  9  inches  for  matching  on 
each  strip  except  the  first. 

73.  A  grocer  pays  $16  for  5  bushels  of  cranberries,  and 
sells  them  so  as  to  gain  30%.  What  is  the  selling  price  per 
quart  ? 

74.  I  loaned  $450  at  5%,  and  received  $502.50  when  it 
was  paid.     For  how  long  was  it  loaned  ? 

75.  The  face  of  one  side  of  a  cube  is  a  surface  of  100 
square  feet.     Find  the  volume. 

76.  A  tax  of  $6181.40  is  to  be  assessed  upon  a  town. 
There  are  620  persons  subject  to  a  poll  tax  of  $1.25  each. 
The  property  assessment  is  $675800.  Find  the 'tax  on  Mr. 
Anderson's  property,  which  is  assessed  at  $4750  if  he  pays 
for  one  poll. 

77.  A  man  buys  a  house  and  lot  for  $3500  ;  he  pays  $1000 
cash  and  gives  a  mortgage  for  the  balance  at  6%.  At  the 
end  of  9  months  he  sells  the  house  and  lot  for  $4500,  paying 
the  interest  due  on  the  mortgage  at  the  time  of  sale.  How 
much  does  he  realize  on  his  investment  ? 


GENERAL    REVIEW  413 

78.  I  desire  to  invest  #9000.  I  can  buy  7%  stock  at 
20%  premium  or  loan  the  money  at  t>%.  Which  is  the 
better,  both  being  safe  investments? 

79.  Solve  the  following  equations : 

6%  of  $100  =  5%  of  ($       ). 
37*%  of      64  =  (     %)  of  120. 

80.  SI 650  yields  8530.75  interest  in  5  years,  4  months, 
10  days.     Find  the  rate. 

81.  What  sum  of  money,  at  6%  simple  interest,  will 
produce  in  2  years,  6  months,  the  same  interest  that  $900 
will  produce  in  3  years,  4  months,  at  5  %  ? 

82.  The  slant  height  of  a  church  spire  is  48  feet,  and  its 
base  is  a  hexagon  6  feet  on  each  side.  Find  the  cost  of 
painting  it  at  40^  a  square  yard. 

83.  On  a  bill  of  goods  amounting  to  $900,  I  am  offered 
a  discount  of  25%,  or  two  successive  discounts  of  15%  and 
10  % .  Which  would  be  more  advantageous  for  me  to  accept, 
and  how  much  more  ? 

84.  My  gas  meter,  Jan.  1,  registered  11800  cu.  ft.;  Feb.  1, 
35800  cu.  ft.  I  paid  the  bill  before  Feb.  10,  receiving  a  dis- 
count of  2  ^  on  the  even  thousand.  At  27  /  a  thousand  cubic 
feet,  how  much  did  I  pay  for  the  gas  used  in  January? 

85.  Simplify:  a.  JL^^g^     J.  gf^  x  ^ 

86.  I  imported  from  Canada  7500  yards  of  flannel  valued 
at  80^  a  yard,  and  weighing  1480  pounds.  Specific  duty 
22^  per  pound,  and  ad  valorem  duty  30  % .  Find  the  amount 
of  duty  paid. 

87.  The  taxes  on  a  property  last  year  were  $42,  which 
were  |  less  than  this  year.  Find  the  per  cent  of  increase  in 
taxes. 


414  GENERAL   REVIEW 

88.  A  street  £  mile  long  and  30  feet  wide  is  paved  and 
curbed.  The  paving  costs  $  3  a  square  yard,  and  the  curb- 
ing 30  ^  a  linear  foot.     Find  the  entire  cost. 

89.  Find  the  sum  of  the  quotients : 

.01-*-.  001  .1  -10  .001  +  . 1 

10+. 01  .01  +  10  .01   +.001 

90.  The  specific  gravity  of  milk  is  1.032.  Find  the 
weight  of  18  gallons  of  milk. 

91.  A  hotel  and  farm  sold  for  $6000  each.  The  hotel 
was  sold  at  a  gain  of  20%,  and  the  farm  at  a  loss  of  20%. 
Find  the  gain  or  loss  on  both  sales. 

92.  The  cost  of  insuring  a  dwelling  at  f  %  is  $33.75  a 
year,  and  the  cost  of  insuring  the  furniture  at  1  %  is  $12.75. 
Find  the  amount  of  each  policy. 

93.  Which  produces  the  greater  per  cent  of  income  and 
how  much,  4  %  bonds  at  75  or  5  %  bonds  at  90? 

94.  Find  the  sum  of  the  square  roots  of : 

.5625  226.5025  110J 

.0016  100.2001  148|i 

95.  I  bought  stock  at  89 J,  brokerage  |  %,  and  after  receiv- 
•  ing  a  dividend  of  4%,  sold  at  104|,  brokerage  \%  clearing 

$150.     Find  the  amount  of  stock  purchased. 

96.  A  town  expends  for  improvements  $6894.  The 
assessed  valuation  is  $480000.  Find  the  rate  levied  to  cover 
the  expense,  including  the  collector's  commission  estimated 
at  $306. 

97.  A  swimming  pool  is  30  meters  long,  14  meters  wide, 
and  averages  1.5  meters  in  depth.  Find  the  number  of 
kiloliters  of  water  it  contains  and  its  weight  in  kilograms. 


GENERAL    REVIEW  U5 

98.  A  Mexican  ranchman  purchased  a  tract  of  land  in  the 
form  of  a  rectangle  10  kilometers  in  length  and  4  kilometers 
in  width.      Find  the  number  of  acres  in  it. 

99.  The  oxygen  in  the  air  is  to  the  nitrogen  as  21  to  79. 
Find  the  number  of  cubic  feet  of  each  gas  in  a  schoolroom 
whose  inside  dimensions  are  30  ft.  x  24  ft.  x  12£  ft. 

100.  What  sum  will  cancel  a  note  for  $122.50  bearing  in- 
terest at  6%,  dated  April  10,  1903,  and  maturing  September 
4,  1905  ? 

101.  A  garrison  of  800  men  have  provisions  for  90  days. 
A  reenforcement  arrives  at  the  end  of  40  days,  and  the  pro- 
visions last  only  40  days  longer.  Find  the  number  of  the 
reenforcement. 

102.  Simplify:    ^-A^xfofii-^J- 

103.  What  decimal  bears  the  same  ratio  to  .05  that  f  does 
toll? 

104.  A  savings  bank  pays  4  %  interest  compounded  semi- 
annually, the  interest  periods  being  April  1,  and  October  1. 
I  deposited  $100,  April  1,  1903,  and  an  equal  amount  semi- 
annually to  and  including  October  1,  1905.  What  amount 
had  I  on  deposit  April  1,  1906? 

105.  An  insolvent  debtor  pays  40  cents  on  the  dollar. 
How  much  will  a  creditor  receive  whose  claim  is  $960,  after 
paying  his  attorney  10  %  for  collecting  it  ? 

106.  A  rectangular  field  whose  width  is  f  of  its  length 
contains  7|  acres.  Find  the  distance  between  the  opposite 
corners. 

107.  I  loaned  f  of  a  certain  sum  at  6%,  and  the  remain- 
der at  5%.  The  entire  income  was  $322.50.  Find  the  sum 
loaned. 


416  GENERAL   REVIEW 

108.  A  gentleman  wishes  to  invest  in  4|  %  bonds,  selling 
at  102,  so  as  to  provide  for  a  permanent  income  of  -$1620. 
How  much  should  he  invest  ? 

109.  From  one  tenth  take  one  thousandth ;  multiply  the 
remainder  by  10000 ;  divide  the  product  by  one  million,  and 
write  the  answer  in  words. 

no.  A  drugget  9  ft.  by  12  ft.  covers  50%  of  the  floor  of 
a  room  13|  ft.  wide.     Find  the  length  of  the  room. 

ill.  A  mechanic  had  his  wages  twice  increased  10%. 
Find  his  wages  before  the  first  increase,  if  he  now  receives 
$4.84  per  day. 

112.  A  house  which  had  been  insured  for  13000  for  9 
years  at  If  %  for  a  term  of  three  years  was  destroyed  by  fire. 
How  much  did  the  money  received  exceed  the  premiums 
paid  ? 

•113.  A  natural  gas  company  declares  a  semiannual  divi- 
dend of  4  %  on  a  capital  stock  of  $150,000.  Find  the  yearly 
dividend  of  a  stockholder  who  owns  36  shares,  par  value 
$50  a  share. 

114.  A  merchant  in  Denver,  Col.,  buys  a  New  York  draft 
for  $600,  at  \%  exchange,  and  mails  it  in  payment  of  a  bill 
in  Memphis,  Tenn.     Find  the  amount  paid  for  the  draft. 

115.  How  long  must  $120  be  at  interest  at  6%  to  earn 
$34.64? 

116.  If  a  clerk's  wages  are  $48  a  month,  when  he  works 
8  hours  a  day,  how  much  should  he  receive  for  9  months' 
work,  of  10  hours  a  day  ? 

117.  Each  side  of  a  roof  is  30  ft.  long  and  18  ft.  wide. 
How  many  shingles  16  in.  long  and  4  in.  wide,  laid  \  to 
the  weather,  will  be  required  to  cover  the  roof? 


GENERAL    REVIEW  417 

118.  City  bonds  bearing  4%  interest  are  sold  at  12% 
premium.  Find  the  rate  per  cent  the  buyer  gets  on  his 
investment. 

119.  The  capital  stock  of  a  company  is  $50,000.  There 
is  a  deficit  of  $  4000  in  the  earnings.  I  own  80  shares.  Find 
the  amount  1  must  pay  if  an  assessment  is  levied. 

120.  A  lawyer  in  collecting  a  note  of  $  3000,  compromised 
by  taking  80  %  and  charged  5  %  for  his  fee.  Find  his  com- 
mission. 

121.  A  man's  income  is  *-  of  his  capital.  His  taxes  are 
2|  (f0  of  his  income.  Find  the  amount  of  his  capital  if  he 
pays  $  24  taxes. 

122.  The  specific  gravity  of  iron  is  7.80.  Find  the  weight 
of  an  iron  bar  12  ft.  long  and  2  in.  square. 

123.  Find  the  result  of  C°5  *  1.25+ .1875)  x  96  _16>5# 

(.4 -5 +.17) 

124.  The  inside  measure  of  a  cubical  box  is  4  in.  on  each 
side.  A  sphere  4  in.  in  diameter  is  placed  in  the  box.  Find 
the  per  cent  of  space  unfilled. 

125.  At  $1£  a  rod,  it  cost  $240  to  fence  a  square  field. 
Find  the  cost  of  fencing  a  rectangular  field  of  equal  area 
wmose  sides  are  to  each  other  as  1  is  to  4. 

126.  A  piano  listed  at  $  650  was  sold  at  a  discount  of  40  % 
and  20  %.  If  the  freight  was  $3.25  and  dray  age  $5,  what 
was  the  net  cost  of  the  piano? 

127.  A  merchant  sold  a  bill  of  goods  amounting  to  $  3600 
and  took  a  90-day  note  for  it.  Fifteen  days  later  he  sold  the 
note  at  a  bank  at  6  %  discount.  How  much  did  he  receive 
for  the  note  ? 

128.  A  boat  in  crossing  a  river  400  feet  wide,  drifted  with 
the  current  300  feet.     How  far  did  the  boat  go? 

HAH.    COM  PL.     Altllll.  — 27 


418  GENERAL   REVIEW 

129.  Mr.  Brown  owed  Mr.  Smith  $2000  which  he  was 
unable  to  pay  ;  but  he  gave  him  two  90-day  notes  covering 
the  amount.  One  was  for  $1000  without  interest;  the  other 
with  interest  at  6%.  Mr.  Smith  had  both  notes  discounted 
at  a  bank  at  7  %  on  the  day  they  were  given.  How  much 
cash  did  he  receive  ? 

130.  A  merchant  owing  a  bill  of  $1250  in  New  York  is 
asked  to  send  a  draft  in  settlement  of  the  account.  The 
merchant  has  only  $868  in  bank  and  holds  a  note  of  $900 
due  in  30  days  without  interest.  This  he  has  discounted  at 
6  %  for  20  days  and  the  proceeds  is  placed  to  his  credit.  He 
buys  a  draft  at  |  %  exchange,  giving  his  check  for  the 
amount.     How  much  does  he  then  have  in  bank? 

131.  Mr.  Franks  has  a  promissory  note  of  $800  dated  July 
1,  1906,  due  in  one  year  with  interest  at  6%,  against  Boyd 
Emerson,  on  which  are  the  following  endorsements : 

Jan.  1,  1907,  $50.00  Jan.  1,  1908,  $150.00 

Dec.  1,  1907,    25.00  Apr.  1,  1908,   200.00 

Write  the  note  with  the  indorsements  and  find  the  balance 
due  Aug.  1,  1908. 

132.  A  San  Francisco  banker  discounts  a  draft  for  $3000 
payable  at  Portland,  Oregon,  90  days  after  sight.  Exchange 
-Jg  %,  discount  8  %.     Find  the  proceeds. 

133.  The  United  States  government  pays  exact  interest 
at  5  %  from  April  1  to  Oct.  10  on  a  claim  of  $63500.  Find 
the  interest  the  government  pays. 

134.  Find  the  cost  of  carpeting  a  hall  30  ft.  by  50  ft  with 
carpet  27  inches  wide,  laid  lengthwise,  at  $1.10  per  yd.,  sur- 
rounded by  a  carpet  border  18  inches  wide,  at  $  1.10  per  yd., 
allowing  6  inches  for  matching  on  each  strip  except  the  first. 


GENERAL    REVIEW  419 

135.  A  cable  message  was  sent  at  6:15  a.m.  from  New 
York  to  London.  It  was  delivered  28  minutes  20  seconds 
after  being  sent.     At  what  time  was  it  delivered? 

136.  Mr.  Coll  leased  some  property  for  three  years  at 
$2400  per  year.  His  commission  for  leasing  was  1  %  of  the 
first  year's  rent  and  his  commission  for  collecting  5  %  of  each 
year's  rent.  Find  the  agent's  entire  commission  for  the 
three  years,  if  all  the  rent  was  collected. 

137.  A  commission  merchant  was  offered  $1800  per  year 
salary  and  2  %  on  all  sales  above  $40000,  or  5  %  on  all  salts. 
He  chose  the  latter  and  sold  $85000  worth  of  goods.  Did 
he  gain  or  lose,  and  how  much,  by  so  doing  ? 

138.  2000  yards  of  silk  when  imported  cost  215  ^  per 
meter.     If  sold  at  $2.25  per  yard,  find  the  gain. 

139.  A  railroad  tank  along  the  line  of  the  Paris  and  Lyons 
railway  is  3.5  meters  in  diameter  and  6  meters  in  height. 
Find  the  number  of  kiloliters  it  contains. 

140.  The  specific  gravity  of  iron  is  7.80.  Find  the  weight 
in  kilograms  of  a  bar  of  iron  1  meter  long,  1  decimeter  wide, 
and  5  centimeters  in  thickness. 

141.  A  bookkeeper's  income  is  $2700  per  year.  His 
expenses  average  $50  per  month.  If  he  deposits  the  bal- 
ance every  six  months  in  a  savings  bank,  how  much  will  he 
have  in  the  bank,  at  4  %  interest,  compounded  semiannually, 
after  3  deposits  ? 

142.  A  ship  sets  sail  at  Seattle,  Nov.  15,  at  1  p.m.,  120th 
meridian  time,  and  arrives  at  Canton  in  21  da.  5  hr.  18  niin. 
Find  the  solar  time  of  arrival  in  Canton. 

143.  Sound  travels  1120  ft.  per  second.  The  thunder  from 
a  flash  of  lightning  was  heard  8  seconds  after  the  flash  was 
seen.     How  far  distant  was  the  cloud  ? 


420  GENERAL   REVIEW 

144.  At  what  price  must  a  bank  stock  paying  6  %  annual 
dividends  be  purchased  so  as  to  net  the  purchaser  5  %  income 
on  his  investment  ? 

145.  An  agent's  commission  at  2\  %  is  $57.85.  What 
must  be  the  amount  of  a  check  mailed  to  cover  the  purchase  ? 

146.  A  railway  company  declared  a  If.  %  quarterly  divi- 
dend. How  much  did  the  purchaser  pay  for  the  stock,  if  it 
yielded  him  10  %  on  the  amount  invested  ? 

147.  Ames  Bros.,  brokers,  bought  for  me  10  shares  of 
Delaware  &  Hudson,  selling  at  129|  %  premium,  par  $  100. 
Write  the  check  in  payment  to  Ames  Bros,  for  the  stock. 

148.  A  clerk  made  the  following  deposits  in  a  savings 
bank,  at  4  %  interest,  payable  January  1  and  July  1 :  January 
1,  1906,  $500  ;  July  1,  1906,  $350 ;  July  1,  1907,  $200.  On 
January  2,  1907  he  drew  out  $100.  What  was  his  balance 
July  1,  1908? 

149.  In  one  section  of  the  Bessemer  Railroad  there  was 
laid  in  one  year  6  miles  of  double  track.  The  rails  weighed 
100  pounds  to  the  yard  and  the  market  price  was  $32.50 
per  long  ton.  The  ties  cost  delivered  69  cents  each  and 
were  laid  on  an  average  of  one  tie  to  every  two  feet.  Find 
the  cost  of  the  rails  and  ties. 

* 

150.  A  commission  broker  was  to  receive  5  %  on  the  first 
$  50000  from  a  sale  of  coal  land  and  2  %  for  the  remaining 
amount  of  the  sale.  His  entire  commission  amounted  to 
$  4000.     Find  the  total  amount  of  the  sale. 

151.  Mr.  Adams  bought  a  property  for  $  20000.  He  ex- 
pended $4000  in  improvements.  The  repairs  each  year 
averaged  $  250,  the  insurance  and  taxes  2^  %  on  |  of  the 
original  cost  of  the  property.  For  how  much  a  year  must 
lie  rent  the  property  to  realize  6  %  net  on  his  investment  ? 


OPTIONAL   SUBJECTS 

PRESENT  WORTH   AND   TRUE   DISCOUNT 

A  owes  B  $  106,  due  in  one  year  without  interest.  If  A 
pays  the  debt  to-day,  $100  will  cancel  it,  since  $100  at  6  % 
will  amount  to  $106  when  the  debt  is  due.  $106  is  the 
debt;  $100  is  the  present  worth;  and  $106  minus  $100,  or 
$6,  is  the  true  discount. 

The  present  worth  of  a  debt,  due  at  a  future  time  without 
interest,  is  a  sum  of  money  which,  at  a  given  interest,  will 
amount  to  the  debt  when  it  becomes  due. 

The  true  discount  is  the  difference  between  the  debt  and 
its  present  worth.     True  discount  is  seldom  used  in  business. 

Written  Work 

l.    Find  the  present  worth  and  true  discount  of  a  debt  of 

$287.50,  due  in  2  yr.  6  mo.  without  interest,  money  being 

worth  6  %. 

$.15  =  the  interest  of  $1  for  2$  yr.  at  6  %. 
$1.00  +  $.15  =  $1.15  =  the  amount  of  $1  for  2£  yr.  at  6%. 
$287.50-  $1.15  =  250,  and 

250  x  $1.00  =  $250,  the  present  worth  of  $287.50. 
Since  the  present  worth  of  $1.15  is  $1,  the  present  worth  of  $287.50, 
which  is  250  times  $1.15,  is  250  times  $1  =  $250. 

$287.50  -  $250.00  =  $37.50,  the  true  discount. 

Comparative  Study- 
Bank  Discount  is  the  interest  paid  in  advance  upon  the  value  of  a  note, 
or  a  debt,  at  maturity;  true  discount  is  the  interest  on  the  present  worth  of 
the  note,  or  debt,  for  the  given  time.     In  bank  discount  notes  may,  or  may 
not,  bear  interest ;  in  true  discount  debts  are  without  interest. 

The  present  worth  corresponds  to  the  principal;  the  true  discount,  to 
the  interest:  the  sum  due  at  a  future  time,  to  the  amount. 

121 


422  OPTIONAL  SUBJECTS 

2.  What  principal  will,  in  3  yr.  and  6  mo.,  at  6$>,  amount 
to  $344.85  ?  (The  principal  is  the  present  worth ;  the  interest 
is  the  true  discount.) 

3.  Find  the  present  worth  of  1517.50,  due  in  2  yr.  and 
6  mo.,  without  interest,  money  being  worth  G  %. 

4.  A  merchant  buys  goods  amounting  to  $355.25  and 
agrees  to  pay  for  them  in  3  mo.  What  cash  sum  will  pay 
the  bill,  money  being  worth  6  %  ? 

5.  A  farmer  is  offered  $5000  for  his  farm,  or  $5600,  pay- 
able one  half  in  cash  and  the  balance  in  1  yr.  without  interest. 
How  much  is  the  second  offer  better  than  the  first,  money 
being  worth  6  %  ? 

6.  Find  the  true  discount  of  $1350,  due  in  1  yr.,  4  mo., 
without  interest,  money  being  worth  6  %. 

7.  What  is  the  difference  between  the  true  discount  of 
$575  due  in  2-|  yr.  without  interest,  money  being  worth  0%, 
and  the  simple  interest  of  $575  for  2^  yr.  at  6  %  ? 

8.  A  purchaser  is  offered  a  horse  for  $195  cash,  or  $206 
due  in  6  mo.  without  interest.  Which  is  the  better  offer  and 
how  much  ? 

FOREIGN  EXCHANGE 

Foreign  exchange  is  a  method  of  paying  or  collecting  bills 
in  foreign  countries  without  the  actual  transfer  of  money. 

A  bill  may  be  paid  in  a  foreign  country  by  a  postal  money  order,  by 
an  international  express  money  order,  by  a  telegraphic  money  order,  or 
by  a  foreign  draft,  called  a  bill  of  exchange. 

Bills  of  exchange  are  usually  issued  in  duplicate  and  numbered  first 
and  second  of  exchange.  By  sending  them  by  different  mails,  the  payee 
is  almost  certain  to  receive  one.  Each  contains  a  condition  that  it  shall 
be  void  after  the  other  is  paid. 

Bills  in  foreign  countries  are  collected  by  commercial  drafts  in  the 
same  manner  as  in  domestic  exchange. 


FOREIGN    EXCHANGE  423 

A  foreign  draft,  or  bill  of  exchange,  is  similar  to  a  domestic  l>ank 
draft  and  is  payable  in  the  money  of  the  country  on  which  it  is  drawn. 
'I'll  us.  a  bill  of  exchange  on  Paris  is  payable  in  francs. 

Premium  and  discount. 

In  domestic  exchange,  there  is  practically  no  premium  or 
discount  on  money,  except  during  financial  panics. 

In  foreign  exchange,  the  premium  or  discount  varies  ac- 
cording to  the  demand  for,  and  the  supply  of,  money. 

English  exchange  is  quoted  as  so  many  dollars  to  the  pound.  Thus, 
a  quotation  of  4.91  means  that  a  foreign  draft  for  £  1  will  cosl  s  L91. 

French  exchange  is  quoted  either  at  so  many  francs  to  the  dollar,  or  at 
so  many  cents  to  the  franc.  Thus,  a  quotation  of  5.8  means  that  a 
draft  for  $1  will  purchase  5.8  francs  ;  or  a  quotation  of  20  JT  means  that, 
a  draft  for  1  franc  will  cost  2QJsf. 

German  exchange  is  quoted  at  so  many  cents  to  the  -i  marks  or  to  the 
mark.  Thus,  a  quotation  of  98  means  that  98  ^  will  purchase  a  draft  for 
4  marks ;  or  a  quotation  of  24.2  means  that  a  draft  for  1  mark  will  cost 
24.2  cents. 

The  par  of  exchange  between  two  countries  is  the  standard  value  of 
the  monetary  unit  of  one  expressed  in  that  of  the  other.  The  English 
par  of  exchange  is  $4.8665.  A  quotation  of  4.90  is  above  par  and  one  of 
4.84  is  below  par.  The  French  par  of  exchange  is  about  5.18^,  or  19.3. 
The  German  par  of  exchange  is  about  95.2,  or  23.8. 

The    following   is  a  newspaper    quotation  of  commercial 

foreign  exchange  : 

60  Days  Demand 

Sterling  4.81  ....  4.87 

Germany,  reichsmarks     .93f      .     .     .     .94| 

France,  francs  5.21  ....  5.18$ 

This  means  that  a  XI  draft  payable  on  demand  will  cost 

8  4.87  ;  or  $4.81  payable  in  60  days. 

Written  Work 
1.    Find   the   cost    of   a  demand    draft,  at    the  quotation 
given,  for  £  2">. 

Cos!  of  £  1  =8  1.87;  cosl  of  a  £  25  draft  =  25  x  1  I. -7  =  9  121.7.".. 


424  OPTIONAL   SUBJECTS 

2.  Find  the  cost  of  a  60-day  draft  for  4480  marks. 

Cost  of  4  marks  =  93|^;  cost  of  4480  marks  =  ^^  x  934/  =$1050. 

4 

3.  Find  the  cost  of  a  60-day  draft  for  3200  francs. 

Cost  of  5.21  francs  =  $1;  cost  of  3200  francs  =  ?=92  x  $1  =  $614.21. 

5.21 

Find  the  cost  of  a  60-day  draft  for : 

4.  £  25  6.    6500  fr.  8.    635.5  M. 

5.  275  M.  7.    £  255.5  9.    398.2  fr. 

10.  Find  the  cost  of  a  sight  draft  on  London  for  £  400, 
at  the  foreign  quotation  given. 

11.  Find  the  face  of  a  demand  bill  of  exchange  on  Paris 
for  $2500,  at  the  foreign  quotation  given. 

12.  What  is  the  cost  of  a  demand  draft  on  Hamburg  for 
1125  marks,  exchange  94|  ? 

13.  What  is  the  cost  of  a  draft  on  Lyons  for  14,000  francs 
at  5.19? 

14.  A  merchant  buys  a  London  draft  60  days  after 
sight  for  £  95.  If  exchange  is  4.82,  rind  the  cost  of  the 
draft, 

15.  How  large  a  bill  of  exchange  on  Berlin  can  be  pur- 
chased for  $1590,  exchange  being  98  ? 

16.  A  mechanic  has  $  1500  with  which  to  purchase  a 
London  draft,  If  exchange  is  4.845,  how  much  is  the  face 
of  the  draft  in  English  money  ? 

17.  An  American  tourist  bought  a  letter  of  credit  on 
London  for  £  300  at  $4.88  and  1  %  commission.  How  much, 
in  United  States  money,  did  this  letter  of  credit  cost  him  ? 
If  lie  drew  £50  in  Paris,  how  many  francs  did  he  get  in 
exchange,  the  pound  being  valued  at  25.2  francs? 


COMPOUND   PROPORTION  425 

COMPOUND  PROPORTION 

A  simple  ratio  is  a  ratio  of  two  numbers  ;  thus,  9:3  is  a 
simple  ratio. 

A  compound  ratio  is  the  produet  of  two  or  more  simple 

..         ,n   qn       ra    on  f-]      6\  [9:31  . 

ratios  ;  thus,  (9:3)  x  (b  :  2),  or  (  -  x  -  j,  or    j  ,,  t9  l  is  a  com- 
pound ratio. 

A  compound   proportion   is  a  proportion   in  which  one  or 

f  9*3] 
both  ratios   are   compound;    thus,   jV^[  =  18:2    is    a  com- 
pound proportion. 

Written  Work 

1.  If  3  men  earn  $24  in  4  days,  how  much  can  6  men 
earn  in  3  days? 

Since  the  answer  is  to  be  dollars,  the  second  ratio  in  this  compound 
proportion  is  $24  :  $  x. 

The  first  ratio  in  this  proportion  is  compound.  If  3  men  earn  $ 24  in 
a  certain  time,  G  men  can  earn  more  in  the  same  time;  x,  then,  repre- 
sents a  larger  sum  than  $24,  and  the  Jim t  simple  ratio  in  the  compound 
ratio  is  3:6.  If  a  given  number  of  men  earn  $24  in  4  days,  in  3  days 
they  will  earn  less;  x,  then,  represents  a  smaller  sum  than  $24,  and  the 
second  simple  ratio  in  the  compound  ratio  is  4 : 3. 

Combining  these  two  ratios,  the  compound  ratio  is  I  .  \  q  1  and  the  com- 

,              ,.       .     f 3 : 6 1        ^oi            m                6  x  3  x  $24      «.,„ 
pound  proportion  is  \  .  . ._,  j-  =  $24  :  x.      1  hen,  x  = T~,~~Z = 

2.  If  6  men  earn  $75  in  5  days,  how  much  can  12  men 
earn  in  3  days  ? 

3.  If  8  men,  in  10  days  of  9  hours  each,  earn  $280,  how 
much  can  9  men  earn  in  5  days  of  8  hours  each  ? 

4.  If  24  men  dig  a  trench  72  rods  long,  3  feet  wide,  and 
5  feet  deep  in  12  days,  how  long  a  trench,  '2\  feet  wide  and 
3  feet  deep,  can  18  men  dig  in  »i  (lavs? 


426  OPTIONAL   SUBJECTS 

CUBE  ROOT 
Comparing  Roots  and  Periods 

The  cubes  of  the  smallest  and  the  largest  integers  com- 
posed of  one,  two,  and  three  figures  are  as  follows : 
l3  =  1  103  =  loco  1003  =  1,000,000 

93  =  729  993  =  970,299  9993  =  997,002,999 

1.  Separate  each  of  these  perfect  cubes  into  periods  of 
three  figures  each,  beginning  at  the  right;  thus,  997 '002' 999. 

2.  How  does  the  number  of  periods  in  each  cube  compare 
with  the  number  of  figures  in  the  corresponding  roots  ? 

The  number  of  periods  of  three  figures  each,  beginning  at 
units,  into  which  a  number  can  be  separated,  equals  the  number 
of  figures  in  the  cube  root  of  the  number. 

Note.  —  The  left-hand  period  may  contain  one,  two,  or  three  figures. 

3.  How  many  figures  are  there  in  the  cube  root  of  46,656? 
1,030,301?     12,326,391?   - 

4.  Cube  25.     25  =  20  +  5  ;  hence,  it  may  be  cubed  in  two 


ays,  thus  : 

25 

20  +  5 

25 

20  +  5 

125          = 

(20  x  5  )  +  52 

50  tens    = 

202+    (20x5) 

625 

202+2(20x5)+52 

25 

20  +  5 

3125 

(202 

X  5)  +  2(20  x  52)  +  53 

1250  tens    = 

203  + 

2(202 

x5)+    (20x52) 

15625  =   203  +  3(202x5)  +  3(20  x52)  +  58 

Or,  representing  the  tens  by  t  and  the  units  by  u,  we  have 

the  formula: 

( r"  +  u  y  =  f  +  3  f'u  +  3  tu1  +  u\ 


CI  BE    HOOT 


427 


253  = 


=  15,625 


Observe  thai  15,625,  tin-  cube  of  25,  is  composed  of  four 
partial  products  : 

,   1  )  f3=2<>3=S 

(2)  Zfiu  =3(202  x  5)=  6000 

(3)  3fna=3(20  x52)  =  1500 

(4)  tfs  =  58=   125 

5.    Find  tbe  cube  root  of  15,625,  or  find  the  edge  of  a  cube 
whose  volume  is  15,625  cubic  units. 

15'625 
203=    8000 

Trial  divisor,  8x202=l:i<"i 
3  x  20  x  5  =    300 
52  =      25 
Complete  divisor, 


1525 


7  625 


7  625 


20 
5 

2^> 


Separate  the  num- 
ber into  periods  of 
three  figures  each. 
Since  15,625  con- 
tains two  periods,  its 
cube  root  is  com- 
posed of  two  figures, 
tens  and  ones.  As 
the  cube  of  tens  is 
thousands,  the  largest  cube  found  in  15  thousands  is  2  tens,  or  20  ones. 
203  =  8000  (1st  partial  product,  or  t3)  as  shown 
in  figure  A;  15,625  —  8000  leaves  a  remainder 
of  7625  (3  t-u  +  3  tu2  +  u*).  The  root  20.  there- 
fore, must  be  so  increased  as  to  exhaust  this 

remainder, 
and  keep  the 
figure  a  per- 
fect cube. 

The  neces- 
sary additions  to  enlarge  A  and  keep  it 
a  cube  are  :  First,  the  three  equal  square 
solids  B.  C,  and  D  (2d  partial  product, 
or  %Pu)\  second,  the  three  equal  rec- 
tangular solids  (p.  £28)  E.  F,  and  G 
(8d  partial  product,  or  3  tu*))  and  third, 
the  small  cube  (p.  428)  H  (4th  partial  product,  or  n3). 

The  sum  of  these  three  additions  is  7625  cubic  units ;  and,  since  the 
square  solids  B,  C,  and  D  (2d  partial  product,  or  3  t*u)  contain  the  greatest 
part  of  the  additions,  their  volume  is  nearly  7r.-_>:>  cubic  units.     If  we 


rr^^^a-:;v:^25Sg^ 

-r- — — - — — 

; 

_  +j 1_ __^ — 

e- — — 

i , , ,  , . .    , 

/> 


a 


.  f    f.  -     --  -    shall  find  their 

H    I  ■  ■_        is  9     i       •  b     '.--    I    -  the  surface  of 

--—  j  j  i  ".'-:.••-■ 

.  iitions. 
1.  C.L.  E    F.  G.  aud  H 
v  -  ic  each  Sraatet]     I    :    -  i  »  ihnne      " " 
cubic  Trnxte)  vould  be  feimil*  i   than 

H<  .      -■     ;  -.    -T 

-r        -  -   '  unite. 
:  •-■       --  "  ii-  -    ..L"-   -   -  _-  .   .-.    i  "  -  -  r* 

•-    •    ■ .     •-  :n  .       '    --.-    I    T 

=^:ji  anc  ei      e        L._ .  -.     ;:-_.,- 

'  ami:-         [    -    -        mite  wide  I    - 

i  .  •     -   mac  rants,  and  the  surface  of  tbe 

'    •  '          - '  -  __ 

-  -i«ft*iMw           -        i          be  UK,  ^  ^^ 

•  . '  -       ■  -  fcb±tf 

T  •  -                                                                 ..iditio:  ..•-.••-  25, 

-  ' . '        .Are  Tir 

-  ■      .  -  -■  ^^m 

'    .'  ■  V:  -.-- 

-  -     -  ..  ~         *= 
uii"*rt      c.'j'.-                -  :  .              -  :  naust          -  -  " 

■Bttfc.  li>  -      -  ".  -      ■  ^^^^^^^^^ 

-       '       -  -  -  '  ■ 

"'■—'       '  -       -       -  "     '         I  "  i 

I 

-      umbere  eaiino;    -    -->••. be     iato  two  or  f/tr*^  -  Kfan; 

l       ■  vd.   art    - 

.'  In  -eacli  case,   one  o: 

.        -   root  of 
-.j*  iiuiD'  regarded  aB 

■e  number  of  unit*  iu  tfce  «<fpe  o/ 
■a  ""Hy  cif  eubie  units  equai  t>o  the  g 


CUBE    ROOT 


129 


6.    Cube  35  (30  +  5)  ;  then  find  the  cube  root  of  42875. 

(1)  f»=308=  27000 

Partial      I  (2)   3  fiu  =  3  ( 31  >2  x  5  )  =  1 3500 

products:     1(3)   3f»2=  3(30  x  52)  =    2250 

(4)  tf3=53=      125 

42875 


42'875 

30 

Trial  divi-                303  = 

= 27000 

5 

sor,       3  X  302  =  2700 

15875 

35 

3  x  30  x  5  =    450 

52  =      25 

Complete  divisor,  3175 

15875 

Study  of  Problems 

1 .  How  many  periods  are  there 
in  42,875  ? 

2.  How  many  figures  are  in 
its  cube  root? 

3.  The  left  period  is  42  (42,000). 
The  largest  cube  found  in  it  is  27 
(27,000),  the  cube  of  the  tens. 

4.  What,  then,  is  the  tens'  figure  of  the  root  ?     (  \/27  =3.) 

5.  Subtract;  annex  the  next  period,  and  the  new  dividend  is  15.s7.">. 
The  cube,  30,  or  3  tens,  is  to  be  so  enlarged  as  to  exhaust  this  remainder 
and  yet  preserve  it  a  cube. 

6.  This  dividend  is  composed  mainly  of  what  partial  product?  (The 
second,  3  fiu)  =  3  (302  x  5) . 

7.  What  factors  in  the  second  partial  product  are  already  known? 
(3  x  302.) 

8.  If  15,875  is  divided  by  (3  x  302)  as  a  trial  divisor,  the  quotient 
(5)  will  be  (approximately)  the  other  factor  in  the  second  partial  product. 

9.  What,  then,  is  probably  the  units'  figure  of  the  root?     (5.) 

10.  Observe  that  the  trial  divisor,  2700,  is  equal  to  three  times  the 
square  of  the  root  found,  considered  as  tens. 

11.  The  first  addition  to  the  trial  divisor  is  3  x  30  x  5,  or  450  (three 
times  the  root  found,  considered  as  tens).  The  second  addition  is  52, 
or  25. 

12.  What,  then,  is  the  complete  divisor? 

3  p  +  3  tu  +  «a  =  3  (30)2  +  (3  x  30  x  5)  +  52  =  3175. 

13.  Multiplying  3175  by  5  gives  15,875 ;  or,  u(3  P  +  3  tu  +  u2)  =  3:*u 
+  3  tu2  +  u*.  This  exactly  exhausts  the  remainder  of  15,875.  Hence,  the 
unite'  figure  of  the  root  is  5,  and  the  cube  root  of  42.875  is  30  I  •>, 
or  35. 


430 


OPTIONAL   SUBJECTS 


7.  Find  the  cube  root  of  34012.224.  (Separate  the  num- 
ber into  periods,  to  the  left  and  right  from  the  decimal 
point.) 

34'012.'224'  |  32.4 
33=  27 


Trial  divisor,      3  x  302  =    2700 
3  x  30  x  2  =      180 

22  = 4 

Complete  divisor, 


2884 


012 


5768 


Trial  divisor,    3  x  3202  =  307200 

3  x  320  x  4  =      3840 

42=  16 

Complete  divisor, 


311056 


1244224 


1244224 


When  the  cube  root  consists  of  more  than  two  figures,  three  times  the 
square  of  the  root  already  found  (considered  as  tens),  is  used  as  a  trial 
divisor  in  finding  the  next  figure  of  the  root. 


8.    Find  the  cube  root  of  5  to  thousandth 

IS. 

5.  |  1.709+ 

13  = 

1 

Trial  divisor,        3  x  102  =    300 

4000 

3  x  10  x  7  =    210 

72=      49 

Complete  divisor,                    559 

3913 

Trial  divisor,      3  x  1702  =  86700 

87000 

Trial  divisor,    3  x  17002  =  8670000 

87000000 

3  x  1700  x  9  =     45900 

92=           81 

Complete  divisor,                  8715981 

78443829 

When  a  ciDher  occurs  in  the  root,  annex  tiro  more  ciphers  to  the  trial 
divisor,  bring  down  the  next  period,  and  proceed  as  before. 


CUBE    ROOT  4:11 

Separate  the  number  into  'periods  of  three  figures  each,  to  the 
left  and  right  from  the  decimal  point. 

Find  the  largest  cube  in  the  left-hand  period,  and  write  its 
root  as  the  first  root  figure  sought.  Subtract  this  cube  from  fin- 
left-hand  period  and  annex  the  next  period  to  the  remainder. 

For  a  trial  divisor,  take  three  times  the  square  of  the  root 
already  found,  considered  as  tens,  or  three  times  the  square 
of  the  root  with  two  naughts  annexed.  Divide  the  dividend  by 
it,  and  the  quotient,  or  the  quotient  diminished,  will  be  the 
second  part  of  the  root. 

To  the  trial  divisor,  add  three  times  the  product  of  the  first 
part  of  the  root,  considered  as  tens,  by  the  second  part,  and 
also  the  square  of  the  second  part.  Their  sum  will  be  the 
complete  divisor.  Multiply  the  complete  divisor  by  the  second 
part  of  the  root,  and  subtract  the  product  from  the  dividend. 

When  other  periods  remain,  take  three  times  the  square  of 
the  root  already  found,  considered  as  tens,  for  a  trial  divisor, 
and  proceed  as  before. 

Note. —  1."  When  a  number  is  not  a  perfect  cube,  annex  periods  of 
naughts,  and  continue  the  work  as  far  as  desired. 

2.  Decimals  are  separated  into  periods  of  three  figures  each,  begin- 
ning at  the  decimal  point  and  passing  to  the  right. 

:!.  To  find  the  cube  root  of  a  common  fraction,  take  the  cube  root  of 
the  numerator  and  the  denominator  separately,  or  reduce  the  fraction 
to  a  decimal  and  then  extract  its  cube  root. 

Find  the  cube  root  of : 

1.  2744  7.  373,248 

2.  4096  8.  941,192 

3.  13,824  9.  1,860,867 

4.  19,683  10.  fife 

5.  32,768  11.  TVW, 

e.  91,125  12.  Ty^ 


13. 

.729 

14. 

15.625 

15. 

39.304 

16. 

2i^ti.981 

17. 

.003375 

18. 

3| 

132  OPTIONAL   SUBJECTS 

Written  Work 

1.  The  volume  of  a  cubical  box  is  5832  cu.  in.     What  is 

its  edge  ? 

Note.  —  Since  the  volume  of  a  cube  is  a  number  of  cubic  units  equal 
to  the  product  of  its  three  equal  dimensions,  the  cube  root  of  the  volume 
of  a  cube  gives  the  length  of  its  edge. 

2.  If  9261  cubic  inches  are  built  into  one  cube,  what  is 
the  area  of  its  base  ? 

3.  Find  the  depth  of  a  cubical  cistern  that  will  contain 
2197  cu.  ft. 

4.  What  is  the  edge  of  a  cubical  box  that  will  contain  50 
bushels  of  2150.42  cu.  in.  each? 

5.  A  box  is  16  ft.  long,  8  ft.  wide,  4  ft.  high.  What  is 
the  edge  of  a  cubical  box  of  the  same  volume  ? 

6.  Find  the  edge  of  a  cube  whose  volume  is  equal  to  the 
volume  of  three  cubes  whose  edges  are  respectively  3,  4,  and 
5  inches. 

Geometry  shows  that : 

The  corresponding  lines  of  similar  solids  are  proportional 
to  the  cube  roots  of  their  volumes. 

7.  If  a  ball  10  in.  in  diameter  weighs  125  lb.,  what  is  the 
diameter  of  a  similar  ball  that  weighs  216  lb.  ? 

8.  Of  two  similar  solids,  one  contains  8  times  the  volume 

of  the  other.     The  diameter  of  the  smaller  is  8|  feet;  what  is 

the  diameter  of  the  other  ? 

Suggestion :   </l  :  #8  =  8£  ft. :  x. 

9.  The  weights  of  two  balls  of  metal  are  as  125  to  343. 
What  is  the  ratio  of  their  diameters  ? 

Suggestion :  D.  of  1st :  D.  of  2d  =  ^125  :  v^43. 

10.  If  a  stack  of  hay  12  ft.  high  contains  8  tons,  how  high 
is  a  similar  stack  that  contains  27  tons  ? 

11.  A  square  grain  bin  which  contains  1200  bushels  of  wheat 
has  a  depth  of  only  J  of  its  width.     Find  its  dimensions. 


REFERENCE  TABLES  OF  MEASURES 


Liquid  Measures 


4  gills 


2  pints 
4  quarts 
1  gal. 

The  gill  is  now  seldom  used. 

The  standard  unit  of  liquid  measure  is  the  gallon. 


=  1  pint 
=  1  quart 
=  1  gallon 
=  4  qt.  =  8  pt. 


1  gallon  =  231  cubic  inches 
1  cubic  foot  =  nearly  7\  gallons 
3H  gallons      =  1  barrel        ]  in  measuring  the  capacity 


63  gallons       =  1  hogshead  J      of  cisterns  and  vats 
1  gallon  of  water  weighs  nearly  S\  pounds 
1  cubic  foot  of  water  weighs  nearly  62  i  pounds 


Dry  Measures 

2  pints    =  1  quart 

8  quarts  =  1  peck 

4  pecks  =  1  bushel 

1  bu.       =4  pk.  =  32  qt.  =  64  pt. 

Our  standard  unit,  the  Win- 
chester bushel,  used  for  measuring 
shelled  grains,  =  2150.42  cu.  in.,  or 
nearly  \\  cubic  feet.  In  form  it 
is  a  cylinder  1SJ-  inches  in  diame- 
ter and  8  inches   deep. 

The  dry  gallon  =  268.8  cu.  in. 

The  heaped  bushel,  used  for 
measuring  corn  in  the  ear,  apples, 
potatoes,  etc.,  =  2747.71  cu.  in.,  or 
nearly  1§  cu.  ft. 

The  standard  English  bushel  = 
2218.102  cu.  in. 


Measures  of  Length 
12  inches     =  1  foot 
3  feet  =  1  yard 

5 1  yards j 
16.i  feet    j 
320  rods 
5280  feet 


1  rod 


1  mile 


1  mi.  =  320  rd.  =  1760  yd.  =  5280 
ft.  =  63360  in. 

The  standard  unit  of  length  is 
the  yard. 

A  nautical  mile  (knot)  =  6080.27 
ft.  or  nearly  1.15  common  miles. 
A  league  =  3  nautical  miles ;  a 
fathom,  used  in  measuring  the 
depth  of  water,  =  6  ft.;  a  hand, 
used  in  measuring  the  height  of 
horses,  =  4  in.     A  furlongs  £  mi. 


II  \M.  compl.   \  l :  I  I  1 1        28 


433 


434  REFERENCE   TABLES   OF   MEASURES 

Measures  of  Surface 

144  square  inches  =  1  square  foot 
'9  square  feet       =  1  square  yard 
30^  square  yards    =  1  square  rod 
160  square  rods  ) 
43560  squai'e  feet  j 
640  acres  =  1  square  mile 

1  mile  square      =  1  section 
36  square  miles    =  1  township 

The  acre  is  not  a  square  unit  like  the  square  foot,  the  square  yard,  etc. 
When  in  the  form  of  a  square,  it  is  nearly  209  feet  on  a  side. 

Surveyors'  Measures 

Surveyors  and  engineers  formerly  used  the  Gunter's  Chain.  It  is  66  feet 
long  and  divided  into  100  links  of  7.92  inches  each.  The  tables  are  as 
follows : 


Length 

7.92  inches  =  1  link 
100  links     =  1  chain 
80  chains  =  1  mile 


Surface 

16  square  rods  =  1  square  chain 
10  square  chains  =  1  acre 


They  now  generally  use  a  steel  tape  50  ft.  to  100  ft.  long  divided  into 
feet  and  tenths  of  a  foot;  or  a  chain  50  ft.  to  100  ft.  long  having  links 
each  a  foot  in  length,  divided  into  tenths  of  a  foot. 

Land  Measure  is  computed  by  dividing  the  number  of  square  feet  of 
surface  by  43560,  the  number  of  square  feet  in  an  acre,  and  changing  the 
decimal  of  an  acre  to  square  rods,  etc. 

Measures  of  Volume 

1728  cubic  inches  =  1  cubic  foot 
27  cubic  feet      =  1  cubic  yard 

A  cubic  yard  of  earth  is  considered  a  load. 

A  cord  of  4  foot  wood  is  a  pile  of  wood  8  feet  long  and  4  feet  high,  the 
sticks  averaging  4  feet  in  length,  making  128  cubic  feet  in  the  pile. 

A  cord  of  short  wood  is  a  pile  of  wood  8  feet  long  and  4  feet  high,  the 
number  of  cords  in  a  pile  being  computed  by  multiplying  the  length  of 
the  pile  in  feet  by  the  height  in  feet,  and  dividing  the  product  by  32. 


REFERENCE  TABLES  OF  MEASURES 


435 


Avoirdupois 

10  ounces  =  1  pound 
100  pounds  =  1  hundredweight 
2000  pounds  =  1  ton 
•J-2  in  pounds  =  1  long  ton 

1  T.  =  20  cwt.  =  2000  lb.  = 

32000  oz. 

The  standard  unit  of  weight  is 
the  pound       =  7000  grains. 
1  Av.  oz.        =  437 £  grains. 

The  long  ton  is  used  in  the  United 
wholesale  transactions  in  coal  and  iron 


Weight 

*  60  pounds  =  1  bu.  of  wheat   or 

potatoes 

*  56  pounds  =1     bu.    of    shelled 

corn  or  rye 
*32  pounds  =  1  bu.  of  oats 
196  pounds  =  1  bbl.  of  flour 
200  pounds  =  1  bbl.  of  beef  or  pork 

*  In  most  states. 

States  custom  houses  and  in  the 
.     The  long  cwt.  =  112  lb. 


.    Troy  Weight 
24  grains  =  1  pennyweight 

20  pennyweights    =  1  ounce 
12  ounces  =  1  pound 

1  pound  =  12  oz.  =  240  pwt.  =  5760  gr. 

The  unit  generally  used  for  weighing  diamonds,  gems,  etc.,  is  the 
carat,  which  is  about  3.2  Troy  grains.  It  is  used  also  to  express  the 
fineness  of  gold.     18  carats  fine  means  ||  pure  gold  and  26?  baser  metal. 

The  Troy  pound  =  5760  grains 
The  Troy  ounce   =  480  grains 


Apothecaries'  Weight 

This     is     used    only    in    filling 

medical    prescriptions. 

20  grains     =  1  scruple  —  sc.  or  3 
:)  scruples  =  1  dram  —  dr.  or  3 
8  drams     =  1  ounce  —  oz.  or  § 

12  ounces    =1  lb.  or  lb 

Counting 
12  things  =  1  dozen  (doz.) 
12  dozen  -  1  gross  (gro.) 
12  gross    =  1  great  gross 
20  things  =  1  score. 


Apothecaries'  Liquid  Measures 
This    is    used    only    in     filling 
medical  prescriptions. 
10  minims  (m)  =  1  fluid  dram  (f5) 
8  fluid  drains    =  1  fluid  ounce  (f^) 
16  fluid  ounces  =  1  pint  (0) 


Stationers'  Measures 

24  sheets  =  1  quire 

20  quires  =  1  ream 

Paper  is  frequently  sold  by  the 

pad  or  hulk  of  100,   500,  or   1000 

sheets,  or  by  the  pound. 


436 


REFERENCE   TABLES   OF   MEASURES 


Measures  of  Time 


60  seconds  =  1  minute 

60  minutes  =  1  hour 

24  hours  =  1  day 

7  days  =  1  week 

12  months  "I 

V  =  1  common  year 

=  1  leap  year 
=  1  decade 
=  1  century 


Thirty  days  have  September, 
April,  June,  and  November. 
All  the  rest  have  thirty-one 
Save  February,  which  alone 
Has  28,  and  one  day  more 
We  add  to  it  one  year  in  four. 


365  days 

366  days 
10  years 

100  years 

The  true  solar  year  is  365  days,  5  hr.,  48  min.,  46  sec.  The  standard 
unit  of  time  is  the  day  which  is  divided  into  24  hours  counting  from 
midnight  to  midnight.  Tn  business  transactions  30  days  are  considered 
a  month,  and  12  months  are  regarded  as  a  year. 

The  centennial  years  divisible  by  400,  and  all  other  years  divisible  by  4, 
are  leap  years. 

Measures  of  Angles  and  Arcs 

60  seconds    =  1  minute 

60  minutes  =  1  degree 
360  degrees    =  1  circumference 
1  right  angle  =  90  degrees 


United  States  Money 

10  mills     =  1  cent 
10  cents    =  1  dime 
10  dimes  =  1  dollar 
10  dollars  =  1  eagle 


English  Money 

4  farthings  =  1  penny    =  $.02025 
12  pence        =  1  shilling  =  §.243 
20  shillings   =  1  pound     =  14.8665 


The  unit  of  English  money  is  the  pound. 

The  value  in  United  States  money  of  other  foreign  coins  is  as  follows : 


Ruble 

Russia                      =  $  .515 

Yen 

Japan                       =     .498 

Franc 

France  (Belgium)  =     .193 

Mark 

Germany                 =     -238 

Crown 

Austria-Hungary   =     .203 

Lira 

Italy                        =     .193 

Peseta 

Spain                        =     .193 

Peso 

Chile                         =     .365 

Crown 

Sweden                     =    .268 

INDEX 


Abbreviations,  109. 
Abstract  number,  24. 
Accident  insurance,  262. 
Accounts,  112-114,  170-174. 
Acre,  192,  193,  356,  434. 
Acute  angle,  196. 
Ad  valorem  duty.  273. 
Addends,  14. 
Addition,  defined,  13. 

of  common  fractions,  52-54. 

of  decimals,  96,  97. 

of  denominate  numbers,  119, 

1S4,  1S5. 
of  integers,  13-18. 
sign  of,  13. 
Agent,  147,  255. 
Agricultural    Problems,    392- 

400. 
Aliquot  parts,  of$l,  108-111. 

interest  by,  '276,  277. 
Altitude.  129,  196,  --"-"2.  368. 
Amount,  in  adding.  14. 
in  interest,  151,  275. 
in  percentage,  23S. 
Analysis,  84-89,  231-230,  345- 

348. 
Angle,  defined,  194. 

measures  of,  195,  190,  436. 
Annual  interest,  286,  287. 
Antecedent,  337. 
Apothecaries'  liquid  measures, 

435. 
Apothecaries'  weight,  435. 
Approximate    measurements, 

224,  385,  3S9,  433. 
Arabic  notation  and  numera- 
tion, 7-lo. 
Arc  measures,  195,  196,  436. 
Are,  387. 
Areas,  124,  129,  199-201,   -'or, 

211. 
Arithmetic,  defined,  7. 
Assessed  valuation,  271. 
Assessment    of    stockholder, 

325. 
Assessors,  269. 
Avoirdupois  weight,  435. 

Balance  of  account,  112,  173, 

174. 
Bank,  303. 

Bank  discount.  307-314,  421. 
Bank  draft.  317. 
Banking.  808-314. 
Barrel,  223,  L"J4,  4.33. 
Base  in  figures,  129.  190. 
Base,  in  percentage,  145,  238. 


Base  line,  350. 

Belgian  money.  181-183. 

Hill  of  exchange,  422. 

of  hiding,  821. 
Billions,  8,  9. 

Bills  and  accounts,  160-174. 
Bins,  2i':;. 

Blank  indorsement,  294. 
Board  font,  135,  130,  217. 
Bonds,  331-334. 
Borrowing  from    banks,   307- 

bl4. 
Brickwork.  220,  221. 
Broker.  'J.'"'. 

Brokerage,  255-259,  325. 
Bunch  of  shingles,  203. 
Bundle  of  laths,  201. 
Bushel,  115,  '223,  224,  433. 
Business  applications  of  deci- 
mals, 108-111. 

Canadian  money,  182. 
Cancellation,  42,  43. 
Capacity,  common  measures, 
of,  224,  433. 
metric  measures  of,  3SS,  3S9. 
Capital.  324.  342. 
i  apital  stock,  324. 
i  larat,  435. 
Caret  in  division  of  decimals, 

104. 
Carpeting,  204.  205. 
i  ash  discount,  264. 
( lashier,  303. 
Cent,  430. 
Centare,  3S7. 
Center  of  circle,  209. 
Centigram,  3S9. 
Centiliter.  889. 
t  'entime,  1S1. 
Centimeter.  884. 
Central  time,  355. 
i  lentury,  436. 
Certificate  of  stock,  325. 
Certified  check,  317. 
Chain.  434. 
Check.  15-.  304. 

Check  book,  304. 
Circle,  209. 

t  ircumference,  19  I.  210. 
Cisterns,  223. 

eting  bills,  820-823. 
Collector,  255,  269. 
Commercial  bills,  268.  269. 
Commercial     discount,      148, 

264-269. 
Commercial  draft,  212. 

437 


Commission    and    brokers 

147,  255-259. 
Commission  broker,  255. 
Commission  merchant,  255. 

Common  denominator,  51. 
Common  divisor.  40. 
Common  factor,  40. 
Common  fractions.  44-S'». 
Common  multiple,  41. 
Complex  decimal,  95,  107. 
Complex  fraction,  75. 
Composite  number,  88. 
Compound  denominate    num- 
ber, 115,  175. 
Compound  fraction,  00. 
Compound  interest.  288-292. 
t  lompound  proportion,  i25. 
Concrete  number.  24. 
Concrete  work,  220,  221. 
Cones,  369-437 1 ,  373-370. 
Consequent,  337. 
Consignor,  255. 
Convex  surface,  222,368. 
Cud,  of  wood,  137,213,220. 
Corporation,  324. 
Cost.  250. 

Counting  table,  435. 
Coupon  bond,  332 
Credit,  112,  173. 
Creditor,  112,  109. 
Crown,  436. 
Cube,  212. 

Cubes  of  numbers,  358,  426. 
t  !ube  root,  426—432. 
by  factoring,  360. 
Cubic  common  units,  132,  212, 

434. 
Cubic  metric  units,  3S7. 
i  'ustomhouse.  272. 
Customs,  272-271. 
Cylinders.  221  223,  30S-373. 

Date  line,  354. 

Dates,  time  between,  1S5. 

Day,  115,  186. 

Daybook,  173. 

Daj  s  of  grace,  295. 

Debit,  112.  173. 

Debtor,  112.  169. 

1  (ecade,  436. 

Decimal  fractions, 

addition  of,  '.'i',  '.'-, 
business      applications     of. 

108-111. 
compared  with  fractions,  94, 

95. 
defined,  '.">. 


438 


INDEX 


Decimal  fractions, 

division  of,  101-106. 

multiplication  of,  98-101. 

notation  and  numeration  of, 
91-94. 

reduction  of,  95. 

subtraction  of,  96-98. 
Decimal  point,  90. 
Degree,    of   angles   and    arcs. 
194,  196,  436. 

of  longitude,  350,  351. 
Demand  note,  294. 
Denominate    numbers,     115— 

122,  175-191. 
Denominator,  44. 
Deposit  slip,  303,  304. 
Diagonal,  123,  207. 
Diameter,  210. 
Difference,  in  percentage,  238. 

in  subtraction,  19. 

in  time,  120. 
Digits,  38. 
Dime,  12,  382,  436. 
Discount,  bank,  307-314,  421. 

commercial,  264—269. 

on  stocks,  324,  326,  328. 

true,  421. 
Discounting  notes,  303,  308. 
Dividend,  in  division,  29. 

in  insurance,  263. 

in  stocks,  325,  329. 
Divisibility,  tests  of,  3S,  39. 
Division,  denned,  29. 

of  Common  fractions,  6S-74. 

of  decimals,  101-106. 

of  denominate  numbers,  121, 
180,  187. 

of  integers,  29-32. 

sign  of,  29. 
Divisor,  29. 
Dollar,  12,  3S2,  436. 
Domestic  exchange,  315-323. 
Dozen,  25,  435. 
Drachma,  182. 
Draft,  317-323,  422. 
Dram,  435. 
Drawee,  319. 
Drawer,  319. 

Dry  measures,  common,   134, 
433. 

metric,  388,  389. 
Dutiei  or  customs,  272-274. 

Eagle,  436. 
Eastern  time,  355. 
Endowment  policy,  262. 
English  money,  181-183,  436. 
Equality,  sign  of,  13. 
Equations,  analvsis   bv,  231- 

236. 
Equator.  349. 

Equilateral  triangle,  197-36". 
Even  number,  38. 
Evolution,  360-36G,  426-432. 
Exact  divisor,  37. 
Exact  interest,  287. 
Excavations,  132. 
Exchange,  315,  323.  422-424. 


Exponent,  37,  359. 

Express  money  order,  315,  422. 

Extracting  roots,  860-866, 426- 

432. 
Extremes,  338. 

Face,  of  note,  293. 

of  solid,  368. 
Factor,  defined,  37. 
Factoring,  39,  40. 

roots  extracted  by,  361. 
Factors  and  divisors,  37—43. 
Farthing,  181. 
Fathom,  433. 
Feeding  stock,  392-394. 
Fertilizers,  395,  396. 
Figures,  notation  by,  7. 
Fire  insurance,  260. 
Firm,  342. 
Flooring,  202,  203. 
Fluid  dram  and  ounce,  435. 
Foot,  433. 

Feinting  of  account,  174. 
Foreign  exchange,  422. 
Foreign  money,  181-1S3. 
Fractional  parts,  of  fractions, 
65,  66. 

of  integers,  60. 
Fractional  relations,  76,  77. 
Fractional  units,  44.  45. 
Fractions,     common,     44-83, 
106.  107. 

decimal,  90-111. 
Franc,  181,  182,436. 
Free  list,  273. 
French  money,  181-183. 
Full  indorsement,  294. 
Fundamental  processes,  7-35. 
Furlong,  433. 

Gain  and  loss,  249-253. 
Gallon,  115,  223,  224,  433. 
German  money,  182. 
Gill,  433. 

Globe,  369,  375,  376. 
Government  bond,  332. 
Government  land,  356,  357. 
Government     revenue,     272- 

274. 
Grace,  days  of,  295. 
Grain,  435. 
Gram,  383,  389. 
Great  gross,  435. 
Greatest  common  divisor,  40, 

41. 
Greek  money,  182. 
Gross,  435. 
Gross  cost.  250. 
Gunter's  chain,  356. 

Hand,  433. 
Hectare,  387. 
Hectoliter,  389. 
Hexagon,  367. 
Hurher  terms,  47,48. 
Hour,  436. 
House,  342. 
Hundreds,  S. 


Hundredths,  91. 
Hundredweight,  435. 
Hypotenuse,  365. 

Improper  fraction,  45. 

Inch,  433. 

Incomes,    from     stocks    and 

bonds,  329. 
Incomplete  decimal,  H)7. 
Index  of  root,  360. 
Individual  note.  295. 
Indorsements,  15>.  293,  294. 
Indorser  of  note,  293.  294. 
Insurance,  259-263. 
Integer,  37. 
Interest,  annual,  286,  287. 

compound,  288-292. 

exact,  287,  288. 

simple,  151-154,  275-284. 

table  of,  291. 
Interest  term,  289. 
Internal  revenue,  272. 
International  date  line,  354. 
Inverting  terms,  of  fractions, 

72,  73. 
Investments,  291,  329. 
Involution,  35S,  359,  362. 
Isosceles  triangle,  197. 
Italian  money,  1S1-1S3. 

Joint  and  several  note,  295. 

Kilogram  or  kilo,  389. 
Kilometer,  384. 
Knot,  433. 

Land  measures,  356,  357,  387, 

434. 
Lateral  surface,  368. 
Laths,  201. 
Leap  year,  436. 
Least  common   denominator, 

51. 
Least  common  multiple,   41, 

42. 
Ledger,  173. 

Ledger  accounts,  173,  174. 
Length,  common  measures  of, 

123,  192,  193,  433. 
metric  measures  of,  384—386. 
Letters,     notation    by,   892— 

405. 
Life  insurance,  262. 
Life  policy,  262. 
Like  numbers,  14. 
Linear  measures,  433. 
Lines,  194. 
Link,  434. 
Liquid     measures,     common, 

433. 
metric.  388.  3S9. 
Lira,  181,  132,  436. 
List  price.  264. 
Liter,  383,  389. 
Load,  212. 

Long  division,  31,  32. 
Long  ton,  435. 
Longitude  and  time,  349-355. 


INDEX 


139 


Loss,  250. 

Lowest  terms,  48,  49. 

Lumber,  134,  135,  217-220. 

.Milker,  of  check,  305. 

of  imt.'.  298. 
Making  change,  17. 
Murine  Insurance,  260. 
Mark.  182,  186. 
Market  value  of  stock,  324. 
Maturity  of  note,  295,  808. 
Means,  in  proportion,  388. 
Measurements,  practical,  193— 

230. 
Measures,  tables  of,  198,  196, 

212,    224,    884-590,    433- 

486. 
Mensuration,  307-381. 
Merchants'    rule    for     partial 

payments,  302. 
Meridian,  349. 
Meter.  382. 

Metric  system,  382-391. 
Metric  ton,  389. 
Mile,  3S5,  434. 
Mill,  12,  382,  436. 
Millimeter,  384. 
Millions,  8,  9. 
Minim.  435. 
Minuend,  19. 
Minus,  19. 
Minute.  436. 

Mixed  decimal,  92,  101,  102. 
Mixed  number,  45,  49,  50,  56, 

57,  61-65. 
Money  order,  315,  316,  422. 
Months,  of  year,  436. 
Mortgage,  331,  332. 
Mountain  time,  355. 
Multiple,  41. 
Multiplicand,  24. 
Multiplication,  defined,  24. 
of   common    fractions,    58- 

68. 
of  decimals,  9S-101. 
of     denominate     numbers, 

186,  187. 
of  integers,  23-28. 
sign  of,  24. 
Multiplier,  24. 

National  bank,  303. 
Nautical  mile,  433. 
Negotiable  note,  293. 
Net  price,  148,  '-'04. 
Net  proceeds,  147,  250,  255. 
Non-negotiable  note,  293. 
Notation   and    numeration,  of 
common  fractions,  46. 

of  decimals,  '.'1-94. 

of  integers,  7-1  o 
Notes,  promissory,  292-302. 
Number.  7. 

symbol,  Jf,  169. 
Numeration,  7-12.   46,   '.'I   B4, 

392. 
Numerator.  II. 


Obtuse  angle,  196. 
odd  number,  88. 
One  dollar  six  per  cent  inter- 
est method,  281,  2S2. 
<  Operation,  signs  of,  36. 
Orders  for  goods,  167. 
Orders  of  units,  8. 
Ounce,  185. 

Pacific  time,  355. 

Painting.  201. 

Papering  and   carpeting,  204, 

205. 
Par  value  of  stock,  324. 
Parallel  lines.   124,  194. 
Parallelogram.  198,  207. 
Parenthesis,  36. 
Partial  payments,  298-302. 
Partition.  29. 

Partitive  proportion,  H41-344. 
Partnership,  342-344. 
Payee,  293,  319. 
Peck,  433. 
Penny,  181. 
Pennyweight,  435. 
Pentagon,  367. 
Per  cent,  237. 
Percentage,  141-146,  237-274, 

335,  336. 
Perch,  220. 

Perfect  square,  360,  361. 
Perimeter,  193,  369. 
Periods  of  figures,  8. 
Perpendicular,  194. 
Personal  insurance,  262,  263. 
Personal  property,  269. 
Peseta,  181,  182,436. 
Peso,  436. 
Pfennig,  182. 
Pi  (tt),  210,  372,  375. 
Pint,  433. 
Plane,  367. 
Plastering  and   painting,  128, 

201,  202. 
Plus,  13. 
Policy,  259. 
Poll  tax,  269. 

Polygons,  regular,  367,  868. 
Postal  money  order,  315,  422. 
Pound   (sovereign1).    181.    182, 

436. 
in  weight,  115.  435. 
symbol,  $,  169. 
Powers  and  roots,  358-366. 
Practical  measurements.   128- 

140,  192-280. 
Premium,   on    exchange,  259, 

262. 
on  policy  ,  262. 
on  -toeks.  824,  320,  328. 
Present  worth,  421. 
Price  list,  266. 
Prime  factor,  39. 
Prime  meridian,  349. 
Prime  number,  37,  88. 
Principal,  in  Interest,  151,  276. 

consignor),  255. 
Prism,  :o;s-:f7:i. 


Private  bank,  808. 
Problems  in  Interest,  288,  284. 
Proceeds,  net.  147,  250,  255. 
of  note.   808. 

Product,  •.'!. 

Profit  and  loss,  249-268. 
Promissory  notes,  292-302. 
Proper  fraction.  45, 
Property  insurance,  260,  261. 
Proportion,  888  844,  126. 
Protesting  a  note.  294. 
Protractor,  195. 
Public  land,  350,  357. 
Pyramid,  369-371,373-375. 

Quadrilaterals,  L98,  199. 

Quart,  1 88 

Quintal,  889. 

Quire,  435. 

Quotations,     of    stocks     and 

bonds,  333. 
Quotient,  29. 

Radical  sign,  360. 

Radius,  210. 

Range,  356. 

Kate,  of  insurance,  259. 
of  interest,  151,  275. 
of  taxation.  269. 
per  cent,  145,  288. 

Ratio,  337,  338,  425. 

Real  estate  or  real  property, 
269. 

Ream,  435. 

Receipts,  157,  166,  168,  169. 

Reciprocal,  72. 

Rectangles,  124,  198-201. 

Rectangular  solids,  131,  213, 
214. 

Reduction,   of   common   frac- 
tions, 47-52,  106,  107. 
of  decimals  to  common  frac- 
tions, 95. 
of     denominate     numbers, 
116-119,   175-184. 

Registered  bond,  832. 

Regular  polygons,  367,  368. 

Remainder,  in  division.  29. 
in  subtraction,  19. 

Revenue,  government,  272- 
274. 

Reviews,  7S-s3,  107,  122,  138, 
155,  156,  159-105.  1-  191, 
225-280,  247-249,  253,  254, 
284,285,885,886,881,401- 
420. 

Rhomboid,  P.m. 

Rhombus,  199. 

Righl  angle,  124,129,194,  196. 

Right-angled  triangle,  128,  206, 
865,  306. 

Rod,  i 

Roll  of  paper,  204. 

Roman  notation.  11. 

Roofing  and  flooring,  202.  208. 

R 9,  858  360,  426-482. 

Ruble,  1  tfl 


440 


INDEX 


Savings  accounts,  289-291. 

Savings  bank,  303. 

Scalene  triangle,  197. 

Score,  435. 

Scruple,  435. 

Second,  436. 

Section,  192,  357. 

Selling  price,  250. 

Share  of  stock,  324. 

Shilling,  181,  436. 

Shingles,  203. 

Shipper,  255. 

Short  rates,  259. 

Sight  draft,  320,  321. 

Similar  figures,  376-378,  432. 

Similar  fractions,  51. 

Similar  solids,  37S,  379,  432. 

Similar  surfaces,  376-37S. 

Simple    denominate   number, 
115,  175. 

Simple  interest,  275-285. 

Simple  proportion,  338-341. 

Simplification  of  complex  frac- 
tions, 75. 

Six  per  cent  interest  method, 
278-282. 

Slxtv-day  six  per  cent  interest 
"method,  278-280. 

Slant  height,  369. 

Solar  year,  436. 

Solids,    212-216,  36.9-376,   37S, 
379. 
similar,  378,  379,  432. 

Sovereign,  181,  182,  436. 

Spanish  money,  181-183. 

Specific  duty,  273. 

Specific  gravity,  379,  380. 

Sphere,  369,  375,  376. 

Spraying  plants,  397-400. 

Square,  of  numbers,  35S. 
of  roofing  and  flooring,  202. 
(rectangle),  124,  19S,  367. 

Square    common    units,    12S, 
193,  206.  434. 

Square  metric  units,  386. 

Square  root,  360-366. 

Standard  time,  354,  355. 

State  bank,  303. 

Statements,  on  bills,  171. 

Stationers'  measures,  435. 


Stere,  388. 

Sterling  money,  181,  182,  486. 

Stock  broker,  325. 

Stock  company,  324. 

Stockholder,  325. 

Stocks  and  bonds,  324-334. 

Stonework,  220,  221. 

Stub  of  check,  304,  305. 

Subtraction,  defined,  19. 

of  common  fractions,  55-57. 

of  decimals,  96-98. 

of  denominate  numbers,  120, 
184,  185. 

of  integers,  19-22. 

sign  of,  19. 
Subtrahend,  19. 
Sum,  in  addition,  14. 

in  percentage,  238. 
Surfaces,    common    measures 
of,  124,  193,  194,  434. 

metric  measures  of,  386,  387. 

of  solids,  213,  369-372. 

similar,  376-378. 
Surveyors'     linear    measures, 

434. 
Surveyors'    square   measures, 

356,  434. 
Swiss  money,  181-183. 

Tables,  interest,  291. 

of  common  measures,  126, 
193,  196,  212,  223,  224,  356, 
433-436. 

of  life  insurance,  262. 

of  longitude,  350,  351. 

of  metric  measures,  384-390. 

of  money,  181,  182,  436. 

of  specific  gravitv,  380. 
Tanks.  223. 
Tare,  273. 
Tariff,  272. 
Taxes,  269-272. 
Telegraphic  money  order,  316, 

422. 
Tens,  8. 
Tenths,  91. 

Term  of  discount,  308. 
Term  policy,  262. 
Terms,  of  fraction,  44. 

of  ratio,  337. 


Thousands,  8. 

Thousandths,  91. 

Time,  and  longitude,  349-355. 

standard,  354,  355. 
Time  belts,  355. 
Time  discount,  264. 
Time  draft,  320-322. 
Time  measures,  436. 
Time  note,  294. 
Ton,  common,  224,  435. 

metric,  3S9. 
Township,  356. 
Trade  discount,  14S,  264. 
Trapezium,  199,  209. 
Trapezoid,  199,  208. 
Triangle,  128,  196,  367. 
Trillions,  8,  9. 
Troy  weight,  435. 
True  discount,  421. 
Trust  company,  303. 

Unit,  7,  44. 

Unit  of  measure,  175,  199. 

United  States  money,  12,  382, 

436. 
United  States  rule  for  partial 

payments,  298-302. 
Unlike  numbers,  14. 

Vertex  of  triangle,  196. 

of  pyramid,  369. 
Vinculum,  36. 

Volume,  130,  214-216, 368, 372- 
376,  378,  379. 

common  measures,  212,  434. 

metric  measures,  3S7,  388. 

Water,  weight  of,  224,  390. 
Week,  436. 

Weight,    common    measures, 
435. 
metric  measures,  389-391. 
Winchester  bushel,  433. 
Wood  measures,  common,  137, 
217-220,  434. 
metric,  3S6. 

Yard,  115,  384,  385,  433. 
Tear,  436. 
Yen,  436. 


ANSWEES 

Page  11. —  1.  43;  449;  1,000,502;  L492.  2.  90;  1908;  1576;  1801. 
3.  XLI;  LXIII;  LXXXIV  ;  XCIX ;  CVII  ;  CCXVIII ;  DLXXII ; 
DCCXXXV;  CMXCVJ  ;  MCMVII ;  MDLXIV ;   MDCXVI ;  M;  CCLX. 

Page  15.  —  2.  §3603.18.       3.2,595,237.       4.3,303,261.       5.3,996,337. 

Page  16.  —  7.  5182.         8.   5261.  9.  6684.  10.   5269.  11.   2799. 

12.  83,302.     13.  82,276.     14.  76,385.     15.  84,503.      16.  62,872.     17.  71,809. 

Page  18.  — 1.  913  rai.  2.  $11,276.  3:  3,805,074  sq.  mi.  4.  $  2,376,- 
000,000.     5.  $1,254,060,661.     6.  $748,152,215. 

Page  20.  —  7.  5997.       8.  22,962.        9.   27.4:!4.         10.   2600.         11.   7999. 

Page  21. —3.  14.571.      4.36,906.      5.18,393.      6.30,996.       7.38,131. 

8.  28,981.         9.  $329.04.         10.  $379.21.        11.  $561.47.        12.  $194.39. 

13.  $  190.39.        14.  $190.33.        15.300,884.        16.565,065.        17.295,404. 
18.   186,418.       19.  433,983.       20.  225,545.       21.   3,472,273.       22.   2,698,987 
23.  3,12-3,092.       24.  4,197,541.       25.  2,304,902.       26.  2.919.062. 

Page  22.— 1.  2029.  2.   7290.  3.  966,779.  4.    144,752,500  bu. 

5.    A,  81375;  B,  $3075.     6.  $9  gained.      7.8  4800.       8.   52,407,000  sq.  mi. 

9.  James,  86750  ;  Henry,  $11,925  ;  Frank.  $5000. 

Page  27. —2.  6000.    3.  3745.    4.   12.880.   5.  35,000.    6.  21,584.    7.  51,134. 
8  a.  1,574,125;  8  6.2,210,200;  8-'.  3,623,700;  8./.  4,793,050;    8  e .  "lr,.  .700 ; 
8  f.  6,174,425;  %  n.  5.583,325;  8  ft.  5,114,300;  8  i.  6,219,400;   8./.  5,769,650. 
9a.  250,880;  9  b.  352,256;  9  <\  577,536  ;  9d.  763,904  :  9^.  823,296  ;  9/.  984, 
064  ;  9  g.  889,856  ;  9  ft.  815,104  ;  9 «.  991,232  :  9/.  919,552.      10.'.  2.130,4<iu  ; 

10  6.2.099,680;  10  c.  4,918,080  ;  10  d.  6,505,120;  10  e.  7,010,880  ;  10/8,379,- 
920;  10  g.  7,577,680;  10  h.   6,941,120  ;   10  i.   8,440,960  ;   10  j.  7,830,560. 

11  a.  2,364,740;  11  b.  3,320,288;  11  c.  5,433,728  ;  11  d.  7,200,392  ;  11  e.  7,760, 
208  ;  11/.  9,275,572  ;  11  g.  8,387.588  ;   11  ft.  7,682,992  ;   11  i.  9,343,136  ; 

11  j.  8,667,496.     12  a.  2,122,925  ;   12  6.2,980,760;   12  c.  4,887,060  ; 

12  d.  6,464,090  ;  12  e.  6,966,660  ;  12  f.  8,327,065  :  12  g.  7,529,885  ;  12  ft.  6,897,- 
340;  12  i.   8.387.720;  12  j.  7,781,170.   13.  a.   1,934,030;  13  A.  2,715,536; 

13  c.  4,452,216;   13  a".  5,888,924  ;    13  e.  6,346,776  ;    13/.  7,586,134  ; 

13  g.  6.859.886  ;  13  ft.  6,283,624  ;  13  i.  7,641,392  ;  13  j.  708,812.  14  a.  2,073,- 
925;  146.  2,911,960;   14  c.  4,774,060;   14-/.  6,31  i,890  ;   14*.  6,805,860  ; 

14  f.  8,134,865  ;  14  g.  7,356,085  ;  14ft.  6,738,140  ;  14/.  8,194,120;  14./.  7,601,- 
570.  15  a.  1,885,275;  15  6.  2,647,080  ;  15  c.  4,339,980  ;  15  d.  5,740,470  ; 
15^.6,186,780;  15/7,394,895;  15  g.  6,686,955 ;  15  h.  6,125,220  ;  15  /.  7,448,- 
760  ;  15  ).  6,910,110.  16  a.  2,064,125  ;  16  6.  2,898,200  ;  16  c.  4.751,700; 
16  rt\  6,285,050;  16  e.  6,773,700  ;  16/8,096,425;  16  0.7,321,826; 
166.  6,706,300  ;  16 i.  8,155,400;  16j.  7,565,650.  17  a.  2,321,620  ;  176.8,269,- 
744;  17  c.  5,344,464 ;  17  d.  7,069,096  ;  17  e.  7,618,704 ;  17/0,106,486; 
17 g.  8,234,644  ;  17  ft.  7,542,896  ;  17  i.  9,172,768  ;  17  i  8,509,448. 

id 


442  ANSWERS 

Page  28.  — 18.    8155.  19.  $7750.  20.    $866.95.  21.    $84. 

22.  1.254.400  1b.  23.  $3729.38.  24.  $26,020.  25.  48,720  rd.  26.  747  mi. 
27.    $13.65. 

Page  30.  —2.  114,  rem.  2.  3.  127,  rem.  1  ft.  4.  51,  rem.  70.  5  a.  $  101.87 
rem.  10;  5  6.  $67.91,  rem.  2?  ;  5  c.  $50.93,  rem.  3?  ;  5 d.  $40.75;  5e.$33.95 
rem.  5?  ;  5/.  $29.10,  rem.  50  ;  5a.  8  25.40.  rem.  If;  bh.  $22.63,  rem.  80 
57.  $20.37,  rem.  50;  5j.  $18.52.  rem.  30.  6  a.  $339.17;  66.  $226.11 
rem.  10;  6c.  $169.58,  rem.  2f  ;  6d.  $  135. 66,  rem.  if  ;  6  e.  $  113.05,  rem 
4  -  :  6  f.  s  96.90,  rem.  if;  6g.  $84.79,  rem.  2<i  ;  6  h.  $  75.37,  rem.  1  f 
6*.  $67.83,  rem.  40;  6  j.  $61.66,  rem.  80.  7  </.  $  104.53,  rem.  1  0  ;  76. $69.69 
7  c.  $52.26,  rem.  30;  1  d.  $41.81,  rem.  20  ;  7  e.  $34.84,  rem.  30  ;  7/".  $29.86 
rem.50  ;  7  g.  $26.13,  rem.  3  *  :  7  h.  $23.23;  1i.  $20.90,  rem.  7  f  ;  7j.$19.00 
rem.  If.  8a.  $195.04;  8  b.  §  130.02.  rem.  2  f  ;  8c.  $97.52;  8c?.  $78.01 
rem.  30;  8  e.  $65.01,  rem.  20  ;  8  f.  $  55.72,  rem.  if  ;  8  a.  $48.76;  8ft.$43.34 
rem.  2  0;  8  i.  $  39.00,  rem.  80;  8j.  $  35.46,  rem.  20.  9  a.  $  360.46,  rem.  1 0 
9  6.  $240.31;  9  c.  $  180.23,  rem.  1  ?  ;  9(7.  $  144.18,  rem.  3  0  ;  9  c.  $120.15 
rem.  30;  9  7*.  $102.99;  dg.  $90.11,  rem.  50;  9h.  $80.10,  rem.  30 
9  7.  $72.09,  rem.  30  ;  9 }.  $65.53,  rem.  10  0.  10a.  $189.69;  10  6.8126.46 
10c.  $94.84,  rem.20;  10(7.  $75.87,  rem.  30  ;  10  e.  $03.23;  10  f.  $54.10 
rem. 50;  10a.  $  47.42,  rem.  20  ;  10/t.  842.15,  rem.  30  ;  10?.  $37.93 
rem.  80;  10/'.  $34.48,  rem.  10  0.  11a.  8148.67;  116.  $  99.11,  rem.  1 0 
lie.  ft  74.33,  rem.  20  ;  lid.  $59.46.  rem.  4  0  ;  lie.  $49.55,  rem.  40 
11  f.  $42.47,  rem.  50;  11a.  $37.16,  rem.  60;  11  h.  $33.03.  rem.  70 
Hi.  s 29.73,  rem.  4  0  ;  11  j.  $27.03,  rem.  10.  12a.  $213.92  ;  12  6.  $142.61 
rem.  10;  12  c.  $106.96;  12  d.  $85.56,  rem.  40;  12c.  $71.30,  rem.  40 
12/.  $61.12;  12a.  853.48;  12ft.  $47.53,  rem.70;  12i.  $42.78,  rem.  40 
12'/'.  $38.89,  rem.  5  0.  13  a.  $459.03,  rem.  10;  136.  $306.02,  rem.  10 
13c.  $229.51,  rem.  30;  13d.  $  183.01,  rem.  20  ;  13e.  $  153.01,  rem.  10 
13  r.  $131.15,  rem.  20;  Ug.  $  114.75.  rem.  7  0  ;  IZh.  $  102.00,  rem.  7  0 
13V.  $91.80,  rem.  70;  13 j.  $83.46,  rem.  10.  14  a.  $423.56;  14  6.  $282.37 
rem.  10;  14c.  $211.78;  14  d.  $  169.42,  rem.  2  0  ;  14c.  $  141.18,  rem.  40 
14/.  $121.01,  rem.  50;  14  a.  $105.89;  14  h.  $  94.12,  rem.  4  0  ;  14  7.  $84.71, 
rem.  20  ;  14 j.  $77.01,  rem.  10. 

Page  31. —  5.  118,  rem.  15;  11,  rem.  175.  6.  1892,  rem.  5;  756,  rem.  45; 
473,  rem.  5  ;  75,  rem.  345.  7.  2512  ;  1004,  rem.  40  ;  628;  100,  rem.  240. 

8.  4510  ;  1804  ;  1127,  rem.  40  ;  180,  rem.  200.  9.  3703,  rem.  19  ;  1481,  rem. 
29  ;  925,  rem.  79 ;  148,  rem.  79.  10.  20,490,  rem.  5 ;  8196,  rem.  6  ;  5122, 

rem.  45  ;  819,  rem.  305.  11.  39,504,  rem.  0 ;  15,801,  rem.  36  ;  0876,  rem.  6 ; 
1580.  rem.  86.  12.   19,503,  rem.  15  ;   7801.  rem.  25;   4875,  rem.  75 ;   780, 

rem.  75.     13.  49,250;  19,700;  12.312.  rem.  40;  1970. 

2.  12.  3.  25.  4.  32,  rem.  20.  5.  20,  rem.  22.  6.  11,  rem.  4.  7.  105, 
rem.  9.  8.  209,  rem.  3.  9.  41.  10.  32.  11.  32.  12.  26.  13.  31.  14.  43. 
15.   77,  rem.  3.     16.  84,  rem.  70. 

Page  32.  — 17.  62.      18.  45.      19.  41,  rem.  6.      20.  43.      21.41.     22.  41. 

23.  60,  rem.  55.  24.  85,  rem.  57.  25.  81,  rem.  51.  26.  96,  rem.  44. 
27.  77.  rem.  3.  28.  79,  rem.  16.  29.  84,  rem.  70.  30.  84,  rem.  14.  31.  81, 
rem.  78.  32.  91,  rem.  34.  33.  90,  rem.  78.  34.  87,  rem.  77.  35.  108, 
rem.  12.  36.  145,  rem.  14.  37.  83,  rem.  29.  38.  100,  rem.  38.  39.  82, 
rem.  37.     40.   109.  rem.  47.     44  a.  24,120,  rem.  181;     44  b.  18.260,  rem.  301  ; 


ANSWERS  443 

44  c.  9562,  rem.  429;  44  d.  8528,  rem.  117  ;  44  e.  747:1,  rem.  196;  44/.  6669, 
rem.  445  ;  44  y.  8193,  rem.  64  ;    44  h.  7206,  rem.  569  ;    44  i.  12,700,  rem.  41 ; 

44  /  7263,  rem.  271.   45  u.   29,278,  rem.  256;   45/..  -!2,165,  rem.  350; 

45  C.  11,607,  rem.  428;  45  d.  10,351,  rem.  702;  45  e.  9071,  rem.  345; 
45/.  7974,  rem.  :J44;  45  y.  9945,  rem.  155  ;  45  h.  8747,  rem.  701 ;  45  i.  15,416, 
rem.  16;  45/.  8816,  rem.  520.  46(7.  21,882,  rem.  172;  46  b.  16,566,  rem. 
184;  46  c   8075,  rem.  248;  46-/.  7736,  rem.  600;  46  e.  0779,  rem.  713; 

46  f.  5959,  rem.  892  ;  46  g.  7432,  rem.  700;  46  h.  0537,  rem.  859 ;  46  i.  1 1.521, 
rem.  359 ;  46 /.  0589,  rem.  338.  47  a.  32,258,  rem.  197  ;  47  6.  24,421,  rem. 
307  ;  47  c.  12.788.  rem.  653;  47  d.   11,405,  rem.  351  ;  47  e.  9994.  rem.  531  ; 

47  f.  8785,  rem. 901  ;  47 g.  10,957,  rem.  268  ;  47  h.  9638,  rem.  55;  47  i.  10,984, 
rem.  485;  47/  9713,  rem.  771.  48  a.  35,913.  rem.  188;  48  6.  27,188,  rem. 
320;  48  c.  14,237,  rem.  660;  48  d.  12,697,  rem.  540;  48  e.   11,127,  rem.  17; 

48  f.    9781,  rem.  368;  48  g.   12,198,  rem.  650;  48  h.    10,730,  rem.  62; 

48  i.  18,909,  rem.  191;  48/  10,814,  rem.  412.  49  a.    29.045,  rem.  40; 

49  b.   21,988,  rem.  348;  49  c.  11,514,  rem.  636;  49  d.   10,209,  rem.  198; 

49  c.  8998,  rem.  830;  49  f.  7910.  rem.  000;  49</.  9865,  rem.  015;  49  h.  8077, 
rem.  831;  49  i.  15.292,  rem.  472;  49/.  8740,  rem.  160.  50  a.  25,411,  rem. 
250  ;  50  b.   19,238,  rem.  152  ;  50  c.  10.074,  rem.  380  ;  50  d.   8984,  rem.  532  ; 

50  e.  7873,  rem.  259;  50  f.  6921,  rem.  140;  50  g.  8031.  rem.  545;  50  h.  7592, 
rem.  380;  50  i.  13,379,  rem.  493;  50/.  7652,  rem.  124.  51  a.  29,492,  rem. 
169  ;  51  b.   22.327.  rem.  207  ;  51  c.   11,092,  rem.  233;  51  d.   10,427,  rem.  359  ; 

51  e.  9137,  rem.  520 ;   51  f.    8032,  rem.  537 ;   51  y.    10.017,  rem.  612  ; 

51  h.  8811,  rem.  558  ;  51  i.  15,528,  rem.  273  ;  51  /  8880,  rem.  825.  52  a.  18,160, 
rem.  165;  52  b.  13,748,  rem.  253;  52  c  7199,  rem.  521;  52  d.  6420,  rem. 
685;  52  e.   5625,  rem.  555;  52/  4940.  rem.  181;  52  y.   6168,  rem.  493; 

52  /(.  5425.  rem.  820;  52  i.  9561,  rem.  490  ;  52  /.  5468,  rem.  525.  53  a.  12,- 
068,  rem.  343;  53  b.  9137,  rem.  69;  53  c.  4784,  rem.  583;  53  d.  4267,  rem. 
181;  53  e.   3739.  rem.  332;  53  f.   3287,  rem.  159;  53  y.   4099,  rem.  456; 

53  h.   3005,  rem.882  ;  53  i.  6354,'rem.  381  ;  53  j.  3634,  rem.  307. 

Page  33.— 2.  S199.92.   3.  40  hr.  4.  16  da.   5.  §289.50.  6.  §63.58+. 

7.  B,  84800;  A,  85075. 

Page  34.  —  9.  8270.  10.  §217.05.  11.  1710  T.  12.  S 5.30,  gain. 
13.  §1660,  total  sale;  §.87+,  average  cost.  14.  §5247.45. 

Page  35.-2.  f 22.50.  3.  So.   4.  837.50.  5.  §2.40.  6.  -825.  7.  §10. 

Page  36. —1.  44.  2.  37.  3.  144.  4.  2832.   5.  88,894.   6.  546.   7.  8. 

8.  L30.   9.  62.   10.  75.   11.  24.   12.  47.   13.  109.   14.  80.   15.  72. 

16.  137. 

Page  40.  — 2.  5,  5,  5.  3.  2,  3,  5,  7.  4.  3,  3,  5,  5.  5.  24,  52.  6.  38,  5,  7. 
7.  2,  3*,  163.  8.  22,  3,  5,  7,  11.  9.  2,  3,  72,  13.  10.  11,  221.  11.  25,  32,  52. 
12.  2s,  5s,  7,  11.  13.  3*,  52,29.  14.  210,  5s.  15.  2',  5,  101.  16.  3,58,  7)  37. 

17.  24,  3,  53.  13. 

Page  41.— 2.  21.  3.  18.  4.  12.  5.  4.  6.  3.  7.  14.  8.  22.  9.  7. 
10.  17.  11.  144. 

Page  42— 3.  144.   4.  1260.    5.  480.    6.  1400.   7.  420.   8.  96. 

9.  830.  10.  570.  11.  720.  12.  255.  13.  5400.  14.  882.  15.  1080. 
16.  2200. 


444  ANSWERS 

Page  43.— 2.   108.       3.  7.       4.   10.       5.  8.       6.   12.       7-  37.       8.  40  1b. 
9.  80  bu. 

Page  48. -2.  ff       3.  ff       4.  ff       5.  ff.       6.  flfe       7.  ff.       8.  flfe 
9.   Iff     10.   Hi-     11.  f*t-     12-   HI-     13.  fff     14.  |ff.     15-  iff 

Page  49.-3.  |.      4.  &.      5.  f      6.   |.      7.  rV      8.  f      9.    {s.  10.  f 

11.  f     12.   11.     13.   |.     14.  T\.     15.  |.     16.    §.      17.    |f.      18.    r8T.  19.   ih 

20.  ff  21.  T\.  22.  TVr.  23.  TV  24.  if.  25.  ^V  26.  ff  27.  f 
28.  If  29.  f*.  30.  ^  31.  ft  32.  ff.  33.  ft.  34.  |f  35.  £, 
36.  ff.  37.  ff  38.  ff.  39.  &.  40.  f.  41.  ff.  42.  f.  43.  f  44.  if. 
45.  ii.     46.   ff     47.   ff 

Page  50.  — 2.  *£.        3.    -\5-.        4.    J-fi.         5.    *&>         6-    W-        7-    W- 
8.  iff*.     9.  «jp>     10.  tffft.     ii.  i|i..     12.  iff  a.      13.  Jfffi.      14.  ifff*. 

15.  HV-*-  16-    ^tM--       17-    fit*.      18.    HV*-       I9-    ^f3-       20.    a^M. 

21.  iff*.  22.  ^A  23.  ijfi.  24.  i^4A  25.  ^W.  27.  2TV 
28.  47if  29.  136f  30.  0ff  31.  32f.  32.  152".;.  33.  22ff  34.  22. 
35.  18f  36.  25.  37.  24.  38.  15.  39.  21ff  40.  23TV  41.  24. 
42.  10ff  43.  5T9?.  44.  61f  45.  157J§.  46.  45ff.  47.  IlOf  48.  92&. 
49.  183f  50.    112. 

p31yo   ci  9        4         3         5  Q        10        3         2  A       1  5      1  2       T  K       _4_       9_     K 

X-dge   JJ..  <S.      j2,    jj,    iJ.  v>-       13)    xJ)    is-  •*•       igi    iJj    if-  <•»•      24'    54'    24" 

6         4         8         5_  t       _8_      12-7           ft          8  1_0        1            Q        J_B      15        9  Irt  2  3  5 

•      T5'    T5'    3?'  •■      40'    40'    ¥5*        °-       24'  24'    24'         "•      40'    45'   ?0"  1W-  1?'  1  ?'  1  J" 

U12       14        1  lO        24      _6       19           1»  2      3       1          Id.        12      22      19  IB  27  25  21 

•     T>5'   TO'   50'  i#s#     '36'    3?'    36'        x"*  5'    6'    6*       trx'      58'   58"'    58"  ±0'  45'  l3'  43* 

1R16        6          1  I?        85      18      2?                       10        1615      34  1Q2  4  4J.9 

1D-      58"'    58'    58".  Xl-       45"    42'    45"                     i0-      48'    48'    48""  ±C''  50 '  60'  67J" 

On       3  2      35        1  Ol         4  0      4  8      4  5 

^U-     35'  35'  35"  ,4±-      60'    60'    60" 

P,„o    KO  O        10      16      15      20  q        32      15      2.8      12  A        42      36      32      27 

rd5e   •*"■  *■      40'    40'    40'    45-  "•       48'    48»    48"'    4?'  *"       60'   50'   50'    67" 

B         80  96        105      100  fi        250      216      425  7        191      385      5<J.4  Q        24      57      2.5. 

°-     T55'  T50"'  T55'  T20"         "■      437'   4o0'  ¥30"  ••      6  93'    553'    653"  °-      50'    60'  50' 

34  Q  36        126        81        154  Ifl        140      504      12  8       1  0  5  11         3  5      54     J_6_0      39 

55"  «•     535'  535'   535'   552-  ±u-     360'  35~5»  35"0'   367'  *■*••     5c  To'     95'  55" 

19  42        180      243      4.'.4  1  J»        25'      44     J  3  2       66  14.       42      25      27       5_S  IK       JUL 

i4-       756'    T..6'    736'    736-  10'        72   '    T5'      ?5~1    72'         A*'      60'    65'    60'    60"  10"      336' 

1«9      1134      944  Ifi        240      408        36        357  17        10  5_      112        3  0  7  4  10        2  00 

3T5'      :!35~'    S"36"  10,      845'    '8~T5'    5T5'    840"  A  ' "       126'    126'    l55»   T55'  xo'       ^25' 

126      780  1Q         54         64         3S         67 

553-    "I~l~5-       1*'-     T35'    135'  1T5'    135' 

Page  54.-2.    2^.  3.14.      4.    lfff       5.    1T\.        6.    2^.        7.    8^- 

8.  Iff.  9.  lfff  10.  2fa  11.  2^.  12.  2ff-  13-  Iff  i4-  HU- 
15.   2-^-        16.    1T455-  18-    80ff.         19.   3111.         20.    35,V         21.   44Jff. 

22.  92ff  23.  115if.  24.  39^.  25.  70fff.  26.  86fff.  27.  224^. 
28.   22if|.     29.    194^2-  30.    3011  mi.     31.  2~83ird.     32.    7T%.     33.    56^. 

Page  55.-2.    ^.       3.    f       4.    &.       5.    T^.       6.  ff-       7.   A-       8-    iV- 

9.  f     10.    T%\.     11.   fff     12.   Jft.     13.    f^.      14.   §2V      15.    A-      I6-    I- 

17.   1A.     18.    T5? 


r5- 


Page  56.  —19.    ff.     20.    $6. 

2.  4i.  3.  7ff  4.  lOff.  5.  »ff  6.  20ff-  ?•  88ff  8.  39^- 
9.  51  fff  10.  54ff.  11.  68fff.  12.  58ff.  13.  48i|i.  14.  24|i. 
15.  16ff.  16.  20T«^.  17.  37ff.  18.  17T%.  19.  5^.  20.  |8f 
21.    5af 


ANSWERS  445 

Page  57.  — 22.    fa.  23.   Increased  ft.  24.    $41ft;    $434J. 

25.   32£$lb.  ;   6£§lb.  26.  ■  5J  mi.  ;  L|mi.         27.   23?.         28.    lfthr.; 

ftbr.;   Ifbr.         29.    84}f|*         30.    17ft  T. 

Page  60. —  2.  2§.      3.    6J.      4.   (if.      5.   Of.      6.    6§.      7.    252.      8    8i 
9.    105.     10.   36.     11.   54.      12.    41.      13.    9.      14.    126.      15.    81.      16.   4ft. 

17.  2f     18.    3f     19.   2ft.     20.    ISf.     21.    3£.     22.    Iff.     23.    9.      24.    74. 

25.  15f.     26.    27ft.     27.    11£.     28.    51. 

Page  61. —  1.    552,000  T.     2.    23,005,284.     3.   ('.55,200  T. 

Page  62.  —  2.   $328.50.           3.   $7.62.            4.    9192.19.  5.    $90.57. 

6.   $68.43.          7.    8181.86.          8.    $125.38.           9.    $10.11.  10.    $97.95. 

11.   $41.40.         12.   $13.28.         13.   $61.43.         14.    966|  mi.  15.    $85.73. 

16.  $468.31.         17.    $2.66;  $2.34;  $3.44.  18.   $74,131.20. 

Page  63. —19.    $10.12. 

2.   344.       3.    530.       4.   805.       5.    1926.       6.    5832.       7.    3620.       8.    0274. 

9.  4950.       10.    9373.       11.   32.202.       12.    0391.       13.    15,420.       14.   45534. 

15.  12,798.     16.    5173.     17.    13,063^.     18.    16,6724,.     19.    15,449. 

Page  64. —  20.    129,8081-        21.    29,7434.        22.   80,726|.        23.   24,970|. 

24.  19,929f.  25.  33,823'.  26.  31,644.  27.  31,2211  28.  84,458f. 
29.  35,502.  30.  18,836ft.  31.  22,810.  32.  39,201  f.  33.  361,150|. 
34.  410,050|.  35.  198  ft.  36.  $13564,.  37.  $56.  38.  $1.20.  39.  $18. 
40.    190  T.     41.    $15.86.     42.    $109.50.     43.    $170,276.      44.    14.898  lb. 

Page  65.  — 45.   25|  da.      46.   $881.25.      47.   $25,521.88.      48.    2,187,000 
gal.     49.    $105. 

Page  67. -2.    §.     3.    |.     4.    ft.      5.    f.      6.    ft.     7.    ft.     8.    |.     9.   ft. 

10.  U-      11.    ft-      12-    h      13.    ft.       14.    ft.       15.    U.       16.    |i.       17.   i. 

18.  915.     19     5-     20.    10f.     21.    12ft.     22.   Oft.     23.   3.     24.    6f.     25.   5ft, 

26.  5f.  27.  20j£.  28.  45|.  29.  "25f|.  30.  10§§.  32.  118$.  33.  64f. 
34.  108J.  35.  21251.  36.  745(1.  37.  2624;.  38.  9269  ,»ft.  39.  12,222. 
40.    75ft.     41.    86,060.     42.    3430}-3|.     43.    1485f. 

Page  68.  —  44.   450f£  mi.    45.    228 ff  T.     46.  90f|  mi.     47.   $841.50. 

Page  70. -2.    ft.     3.    ft     4.   ft\.'    5.    T|0-.      6.    ft.      ?•    ft.  8.     ,4ft. 

9.    ft.     10.    ft.      11.    jft.      12.    ft.      13.    ft.      14.    ft.      15.    -,-':.  16.    ft. 

17.  ft.     18.  rfft.     19.  f|T.     20.    ft.     21.    ftV-     22.    ,f,.     23.    T§2.  24.   ft^ 

25.  ^.  26.  Tf5.  27.  rife.  28.  ftV  30.  f  31.  f.  32.  ft.  33.  ft. 
34.  ft.  35.  2f.  36.  11.  37.  lft.  38.  Iff  39.  J.  40.  ft.  41.  |f. 
42.    ft.     43.    ft.     44.    ff|.     45.    1$.     46.    f.  "47.    ft. 

Page  71.— 49.    3668^.  50.    1643f|.  51.    816f|.  52.    1375|f 

53.  3306|J.     54.  666^$.     55.  309ft%.     56.  2733ft.     57.  883$  jj.     58.    787^. 

Page  73. —1.   21.     2.    15.     3.    284,.     4.   45$.     5.    57^.     6.    51!,.     7.    L93£. 
8.  293J.     9.   1050.     10.  2058.     11.   1242.     12.  2624.     13.   If     14.    §.     15.  l\. 

16.  U.     17.    lft.      18.    ;.      19.    2ft.      20.    §.      21.    |f      22.    11.      23.    ff 


446 

ANSWERS 

24.    lfc.     25. 
32.   6|.     33. 
40.    2$.     41. 
48.    16.     49. 
56.    f. 

If     26.    1||.     27.    B-     28.    IH- 
lfi.     34.  16f.     35.  Hf.     36.  21f. 
1J.     42.    8f     43.    8*.     44.    Jf. 
ft.     50.    H.     51.   3ft.     52.    3. 

29.    ft7. .   30.    ljf     31.  5$. 

37.  lift.  38.  6£.  39.  14f 
45.  7f£$.  46.  341 L  47.  65. 
53.    f.      54.    3T*ft-      55.   fff 

Page  74. 
6.    9ft.      7. 

pupils.     12. 

—  1.    45  da.         2.    If.        3.    i\. 
9ff.      8.    25gfhr.      9.    6125  gal. 
82.20. 

4.    -55000;    if        5.    85.4:,. 
10.   204^f  min.       11.   3090 

Page  75. 
9.    i,        10. 

16.  "l8|. 

-2.    ft.      3.    ft.      4.    f       5.    i. 
24ff.        11.    7i|.        12.  ft.       13 

fi       91            7         7?              R       1    5 
0.     Zj.           <.     T75.          B.      1T5. 

.    ft.        14.    1ft.       15.    33tf. 

Page  76. 
10.    ft.       11 

-3.   ^.       4.    A.       5.    Tfo.       6. 
.    J.       12.    ftfc.       13.    f|.       14. 

|.       7.    ft.       8.    \\.       9.    ft. 

i 

T5- 

Page  77. 

-3.   96.         4.   539.         5.    4J. 

6.    13*.         7.    1|.         8.    1ft. 

9.    |f.      10.    7.      11.    81300.      12.    314,400.     13.    10,824  books.      14.    64,725 
men.       15.    -34500. 


Page  78. —1.    35.       2 
6.    3  505.        7.    24.        8.    149 
12.   7f£mi.        13.   5365,250. 


Increased  ft. 


16- 


9. 

14.    7 


19 

19 
¥0"' 


.    ff.       4.   25ft.       5.    364.76. 

1*0.    14  da.        11.    160  sq.  rd. 

15.    812,800.         16.    $382.50. 


Page  79. 
22.  354  mi. 
1421  rd. 


17. 


8bu.      18.    82480.      19.    8  43.20.     20.   857.     21.    86408. 

24.    16  da.     25.   104r6ft  mi.  ;  20f££  mi.     26.   30£  rd.  ; 

27.    306.50.       28.    86.30.       29.    108  bu.      30. 


23.    |f. 


300 

3  25- 


Page  80. —31.    812,500.     32.    168  trees.      33.    300.      34.    Ji      35.    5200 
gain.  36.    8  70.         37.    812,  room;    520,  board.  38.    8  16,000,  son's  ; 

514,000,  daughter's.       39.   8900.       40.    131.       41.    8|  hr.       42.   6  doz. 


Page  81.  —  43.    53289.60 
47.    33  ft.     48.    540. 
52.    867.500.     53.    4  A 


44. 


Q7 


45.    8214.50.        46. 
!'s;   8  4 
55.    120  A. 


120  lemons. 


49.    lTi¥.     50.  5  16,000,  B's  ;   8  42,000.  A's.     51.   AJ 
54. 


8 1000  gain  ;  60  A 

Page  82.  —  56.   56000.  57.    7$  da.  58.    37800. 

60.    5  2400.        61.   3  5  per  barrel.        62.    $145i.        63.    860. 


59.   51120. 
64.    2621  lb. 


Page  83.  —65.    8151.05. 


69.    76$  ft.  ; 
123£f|  hr. 

Page  84. 

7.  510  lots. 


601  ft. 


59j  ft. 


72.    18  hr.  ;  8  hr. 

-1.    31.6  T.       2. 
8.  84  sheep. 


66.    a . 81  f  gain.     67.    81075  gain.     68.    35.43. 
67|  ft.  ;  109  ft.      70.    55 JJ.      71.    3906ft  mi.  ; 


8.75.       3.    8120. 
9.  8100. 


4.    10.      5.    f       6.    90. 


Page  85. —  10.  818. 
15.  8250.         16.  $350. 


11.  81.56.        12.  87.80.       18.  821.        14.  $1.86. 
17.  5  lb.  3  oz.         18.  82.17.         20.  32.35. 


Page  86.  —  21.  $70.50.  22.  $11.  23.  \,  ft,  \.  25.  85  pupils.  26.  3450. 
27.  128  cu.  ft.  28.  $1690.  29.  462  cu.  in.  30.  8  50.  31.  56^.  32.  224  bu. 
33.  $770. 


ANSWERS  117 

Page  87.  — 34.  6  da.  35.  $880f.  36.  $600.  37.  2000  bu.  38.  §1200. 
39.    100  da.      40.    34  head.     41.    $1.60.     42.    $81.     44.    35  and  6. 

Page  88.  -45.  $6000.  46.  600  pupils.  47.  300  A.;  200  A.  48.  $  1G0. 
49.    §720.  50.    30.  51.    117.  52.    32.  53.    160  A.  54.    16. 

55.    A,  $35;  H,  8  4:..         56.    $12.         57.    65.         58.    §4000. 

Page  89.  —  59.  *4800.  60.  §180.  61.  f.  62.  $60.  63.  12  da. 
64.  $96.  65.  $1050.  66.  §18.  67.  £.  68.  !,  2,  ,'-',,  |.  69.  §300. 
70.    §4800.      71.    96  gal.       72.    *2.40. 

Page  93.  —  1.  .:JI.  2.  .0075.  3.10.000075.  4.400.045.  5.6006.0066. 
6  81)005  7.  .074(1.  8.  000.000084.  9.  5,000,009.0000400.  10.  .005095. 
11.  8.0017.  12.  .000125.  13.  896.00:101.  14.  1000.001.  15.  18,051.957. 
16  07  0003.  17.  .009864.  18.  2135.000032.  19.  1.000001.  20.  1,000,000.1. 
21.    90,000.071.  22.    1830.11684.  23.   429,000.0040.  24.    7035.97. 

25.    07,375.00035.       26.    .05815.       27.    375.069. 

Page  94.  —  28.  419,863.023456.  29.    81.00921.  30.    2986.0298643. 

31.   3020.00302.       32.    70.07.       33.    8000.008.       34.    645,000,000.000009. 

Page  95. -1.  \.  2.  ft.  3.  5fo.  4.  ft.  5.  J.  6.  |.  7.  ,fo. 
8.  jfa.  11.  f.  12.  ft.  13.  f  14.  rife.  15.  |.  16.  ft.  17.  fc.  18.  ft. 
19.    f.     20.   J.     21.    ft.     22.    ft.     23.    |.     24.    i.     25.    ft.     26.    |f 

Page  96.  — 5.  111.55.  6.  187.64.  7.  66.51.  8.  105.9.  9.  168.507. 
10.  19.079.  11.  179.992.  12.  103.422.  13.  471.0.  14.  1.260.  15.  2.2249. 
16.  210.80.     17.   16.2.     18.  230.4909.     19.  25.823.     20.  45.3407.    21.  35.755. 

Page  97.  —  22.    11.1751.     23.    354.32685.     24.    189.61752.  25.    343.9706. 

26    2. 28-2506.     27.  984.37936.     28.  298.09398.     29.  266.1172.  30.  454.4365. 

31.    858.3827.  32.    47.0625  lb.  33.    23.0875  A.  34.   230.7177. 

35.    §  7154.95.         36.    866.9375  sq.  ft. 

Page  98.  —  37.  .5675.  38.  .0466.  39.  2.4194.  40.  9.993.  41.  19.724. 
42.  33.58.  43.  38.068.  44.  71.125.  45.  113.8909.  46.  .101.  47.  100.192. 
48.    26.483.       49.    .101.       50.   4.3935.       51.    8.2415.       52.    .01.       53.    13.5. 

54.  18.021.       55.   99.91.       56.    58.625  yr.       57.    161.6. 

Page  100.  —  3.    .055.         4.    .0476.         5.    .00081.         6.    3.24.        7.   14.7. 

8.  80.214.  9.  4.25.  10.  .486.  11.  .011055.  12.  911.2.  13.  339. 
14.  2759.1.  15.  719.44.  16.  .0003424.  17.  .030335.  18.  125.472. 
19.  42.504.  20.  .1183952.  21.  2.0736.  22.  42.6725.  23.  1203.03208. 
24.  1.925.  25.  1.296.  26.  6.  27.  7.930.  28.  31.290.  29.  489.00. 
30.  73.8.  31.  2.352.  32.  37.468.  33.  10.7325.  34.  59.2144. 
35.  3135.65.  36.  12.054.  37.  .0428790.  38.  .12.  39.  28.65. 
40.  .000225.  41.  7.762536.  42.  2.75804.  43.  328.252.  44.  .12048. 
45.  .760125.  46.  404.02944.  47.  .01548.  48.  14.8:556.  49.  .04936. 
50.    .000608.       51.    1.006008.      52.    .00025.      53.   30.04812.      54.    §3888.75. 

55.  §1200;  §3000;  §4800.      56.    §20,530.25.      57.   472.44  in.  ;  13.123+ yd. 

Page  102.  —  3.    12.02.     4.   141.6.     5.   6.07.     6.    1.5.     7.   5.06.  8.    .1026. 

9.  .03002.  10.  20.03.  11.  .084.  12.  .061.  13.  .87.  14.  .009.  15.  .076. 
16.  .450.  17.  .15.  18.  50.6.  19.  10.25.  20.  3.002.  21.  200.3.  22.  .904. 
23.    .0906.     24.    .704.     25.    9.2945+.     26.    .0027.     27.    .084.     28.  .0704. 


448 


ANSWERS 


Page  105. —  3.    15.      4.    1.8.      5. 
9.  560.       10.    1.24.       11.    12.5.       12. 
16.    218.       17.    .018.        18.    .0055. 
22.    115.8.      23.    16.4.      24.    .0027. 
28.    111,000.      29.    100.      30.    .0002. 


2.21.      6.   2.05. 

.0207.      13.    .8. 
19.    1,000,000. 
25.    17,500.      26. 
31.    210.      32. 


7.  1200.  8.  .012 
14.    745.      15.    9.7. 

20.  2.5.  21.  2.44. 
.033.      27.    .000011. 

.00137.      33.    .00023. 


34.    125.       35.    2(5.175.       36.    1700.82.       37.    14,096.4043. 


Page  106.  - 
43.   .009.      44. 


--38.   .001. 

570.8108+. 


39.  83  da. 

45.    1.25. 


40. 
46. 


1.  .625.       2.   .6.       3.   .416|.       4.   .3125. 
8.  .59375.     9.   .4375.     10.   .68. 


§.405.      41. 

18.5  sq.  i-d. 

5.  .875. 


88.5.      42.  $18.25. 
47.  §20,000. 
6.  .44.       7.   .5625. 


Page  107. —  11.  .6363+. 


15.  .6296+. 
20.  .7551+. 
25.   1.5882+. 

1.  19.97. 
7.  96.309125. 
12.   104.1635. 


16.   .4736+, 
21.   .5384+. 
26.   .75. 
2.   1.4714.       3. 
8.   16.2921. 
13.   10. 5805  &. 


12.  .2903+. 
17.   1.5714+. 
22.  .4545+. 


13.   .6164+. 

18.   1.4705+. 

23.  .0166+. 


14.   .5471+. 

19.   1.2962+. 

24.  .4615+. 


214.065.      4.  4.9222. 

9.   130.5808.         10 

14.   105.4865.     15 


5.  5.996+.        6.  .02+. 
2.31225.        11.  15.5225. 
16.  245.494275. 


9.7416|. 


Page  109.— 2.  §20.      3.  $6.25.     4.  §60.      5.  §6.25.      6.  §10. 
8.  §200.     9.  §300.     10.  §200.      11.  §100.     12.  $5.37*.     13.  §1000. 


7.  §45. 
14.  §  16. 


Page  110. 

Page  111. 

7.    150  yd. 
12.   1600  lb.: 


•15.  §585.       16.  §528.       17.  $760. 


—  2.  2560  1b.      3.  3000  1b. 
8.  12,800  qt.        9.   800  lb. 
750  bu.  ;  2400  cakes.       13. 


4.  60  1b.      5.   200  yd.     6.  260  yd. 
10.  32  collars.        11.  60  bananas. 
48  yd.  ;  48  lb.       14.  260  lb. 


Page  113.  — 1.  §5.02. 
6.  §0.20. 

Page  114.  —  7.  §6.50. 
11.   §21.65. 

Page  117.  — 3.  248  oz.       4. 
8.  1396  min.         9.   14,608  yd. 


2.  >4.22.         3.  §1.75.        4.  $.90.       5.  §2.80- 


8.  $  10.65. 


9.  $10.60. 


10.  $28.65. 


13. 
19. 
23. 
27. 
30. 
34. 


14,500  lb. 
3  mi.  244  id. 
17  T.  7  cwt. 
119  gal. 
14  bu.  . 
$3.84. 


pk. 


1157  in.   5. 
10.  27  in. 
14.  508  pt.    15.  28  qt. 
J  yd.   20.  1  mi.l  ft,   21. 
24.  3  T.  95  lb.  25.  52  mi. 
28.  221  rd.  4  yd.  1  ft.  6  in. 
31.  2  mi.  44.5  rd.    32. 


176  qt.   6.  56  pt.   7.  1825  lb. 

11.  9600  lb.    12.  465  sec. 

16.  43  pk.    18.  1  rd.  4  yd. 

34  min.  3  sec.   22.  64  lb.  9  oz. 

217  rd.  26.  346  bu.  3  pk.  1  qt. 

29.  1  hr.  54  min.  35  sec. 

min.    33. 


16  hr.  4f 


46 1  gal. 


36.  §26.88. 
41.  3  mi.  40  rd. 


7. 


48 


8. 


3 
IS' 


Page  118.  —35.  §39.83. 
39.  32  mi.  40.  44  mi.  80  rd 
3.  i.   4.  T\-   5.  f   6. 

Page  119.  — 9.  f.  10.  &.    11.  f 

15.  .1.    16.  .09.    17.  .28.    18.  §2.95. 

2.  29  bu.  3  qt,  1  pt.  3.  40  T.  11  cwt.  4  lb 
5.  16  wk.  1  da.  14  hr. 


37.  §41.60.    38.  1920  hr. 


12. 


13.  \.         14.  .7. 
4.  21  yr.  239  da.  1  hr. 


Page  120.  —7.  22  mi.  194  rd 

9.  8  hr.  43  min.  15  sec.  11 
14.  Lee,  58  yr.  2  mo.  20  da.; 
3  mo.  8  da. 


4  yd.  2  ft.  6  in. 
(i  yr.  9  mo.  27  da. 
Grant,  42  yr.  11  mo. 


8.  13  gal.  1  qt.  1  pt. 

12.  15  yr.  16  da. 

12  da.;  dif.  15  yr. 


ANSWERS  '      I  19 

Page  121.  2  10  gal.  3  qt.  1  pt.  3.  77  bu:  2  qt.  4.  152  T.  10  cwt. 
7  lb.  s  oz.  5.    247  wk.  4  da.  6  hr.  6.  280  mi.  216  rd.  1  yd.   1  ft. 

8.  3  wk.  5  da.  it  hr.  9.    26  gal.  3  qt.   1  pt.  10.    9  bu.  3  pk.  4  qt. 
11.  5  yr.  7  mo.  18  da.     12.   14  T.  7  cwt.  24  lb.     13.  $  22. so.     14.  26  rd.  1  yd. 

15.  10  packages. 

Page  122.  —  1.  6  min.  18  sec.  2.  32  bbl.  3.  55$jj  bu.  4.  818.30. 
5.  137  T.  12  cwt.  88  lb.        6.  50  ft.  8  in.         7.    110,340  gal.         8.  35.8605  T. 

9.  3.451b.;  $1.29+.       10.  54  mi.  200  rd.       11.  20,007  doz. 

Page  126.  —20.  272.25  sq.  ft.  21.  2800  sq.  rd.  ;  17*  A.  23.  24,300 
sq.ft.  24.  7200  sq.  in.  25.  10  A.  26.  260  sq.  rd.  '  27.  26rVr  sq.  rd. 
28.   250,470  sq.  ft.  29.  33|  A.;  $2025.  30.  8488  sq.  ft.  31.  $76. 

32.  $170.10.         33.  8  40,425. 

Page  127. —  34.  $6450.  35.  640  A. ;  $54,400.  36.  17?  bu.  37.  8  500; 
$.16|.         38.  $88.32.        39.  40  rd.         40.  (3)  2]^  A.      '  41.    (3)  lf&  A- 

Page  128. —  1.  §3.        2.8  8.        3.  140  sq.  yd.        4.  $29.55.        5.8  181. 

Page  129.  —5.  40  sq.  in.       6.  36  sq.  in.       7.  225  sq.  in.        8.  432  sq.  in. 

9.  10  A. 

Page  133.  — 2.  028  sq.  ft,  3.  120  ft.  4.   $37.21.  5.   8  62.80. 

6.72.       7.  288  cu.  ft.        8.   166$  loads  ;  $  41f .        9.  99  sq.  f t.       10.810,000 
cu.  in.;  3506ft  gal.         11.  8  462. 

Page  134.  — 13.  f|  ;  48  oz.  14.  153$  bu.  15.  4308*$  gal.  16.2800 
sq.  rd.  larger.         17.  4  ft.        18.  04  sq.  ft.  ;  384  sq.  ft. 

Page  135.  — 4.  24  bd.  ft.  5.   9  bd.  ft.  6.  45  bd.  ft,         7.  48  bd.  ft. 

8.  100  bd.  ft.        9.  360  bd.  ft. 

1.  8  200.         2.  812.         3.  8260.40.         4.  8400. 

Page  136. —6.  868.75.  7.  87.17.  8.  $13.44.  9.  82.52.  10.  88.06. 
11.  $67.20.  12.8  40.32.  13.  $58.80.  14.8  26.88.  15.16  ft. 

16.  2112  bd.  ft.         17.  224  bd.  ft.         18.  $25.96. 

Page  137.  — 1.  20  cords.  2.8  440.  3.815.  4.8  44.80.  5.  12$ 
cords. 

Page  138. —1.  540  tiles.         2.  289$  f t.  3.  277$  cu.  yd.  4.  $105. 

5.  1,760,000  times.        6.8  24.        7.  $327.68.        8.  718114  sal.        9.8108. 

10.  $16.33.         11.  50  rd.         12.  8  4.84.         13.   10  rd. 

Page  139—  14.  1728  cakes.         15.  8116.07.         16.  792  bd.  ft.  :  $23.76. 

17.  15  A.         18.  2048  bu.         19.  4847^2  gal.         20.150  ft.  81.  $96.80. 
22.  40  ft.        23.  8  800. 

Page  140.  —25.   400  ft.  ;  202  ft.  :  292  ft.  ;  26  ft.  :  216  ft.  26.  1111$  sq. 

yd.    87.  511$  sq.  yd.         88.  4$  sq.  yd.  29.  88|  sq.  yd.  80.  $90£f 

31.  $137.78.           32.8.22.           33.8120.07.           34.    ^  ft.  35.  $23.11. 

36.  2154f*  gal.                37.  $  10.80.              38.  60  farms.  39.  3000  sods. 
40.  $62.40. 

Page  144. —  2.  375.  3.  21.375.  4.  3.5.  5.  235.2.  6.  320. 

7.  735.         8.  $  16.20. 

Page  145  —9.  312.        10.  $30. 

HAM.  COM  PL.    \UIT1I.  —  29 


450      *  ANSWERS 

Page  146—  12.  ft  12.       13.  2  mo.  14.   18  da.  15.  1  A.        16.  5  A. 

17.  32.  18.  28  horses.  19.  3T\.  20.  9  1b.  21.  ft  If  22.  20. 
23.  ft  200.  24.  §50.  25.  8  words.  26.  ft  .20.  27.280.  28.  §3125. 
29.  ft  60.         30.  90  A.         31.  §400.  32.  $150.  33.  1209  people. 

Page  147.  —  2.  §90.  3.  §79.70.  4.  §97.70.  5.  §70.04.  6.  §76.40. 
7.  ft  118.53.  8.  §532.37.  9.  §  135,  commission  ;   §6615,  net  proceeds. 

10.  §1800.         11.  §456. 

Page  148.  —  1.  §12.  2.  §  12.  3.  §  3.  4.  §  20.  5.  §6.  6.  $7.50. 
7.  §  Hi.         8.  §36.         9.  §5.10.         10.  §3.        11.  §8.         12.  §3. 

1.  §126.56.  2.  §1145.  3.  §  1248.  4.  §174.  5.  §1818.  6.  §180.52. 
7.  §612.85.         8.   §251.01.        9.  §2283.36.        10.  §6436.44.        11.  $176.64. 

12.  §52.90. 

Page  149. —14.  §288.          15.  §267.54.  16.  §157.03.           17.  $6.13. 

18.  §4.59.  19.  8  7.65.  20.  ft  129.60.  21.  §4080.  22.  §1890. 
23.  §1353.75.  24.  §53.55.  25.  §64.60.  26.  §291.60;  §21.00  dif. 
27.  $641.25.        28.  Both,  §360. 

Page  150.—  30.  $6643.     31.  §31.82.     32.  §583.20  ;  §648.     33.  §203.74. 

Page  152.  — 2.  §15.         3.  §128.        4.  §29.25.  5.  §126.  6.   §15. 

7.  §12.        8.  §25.07.        9.  §18.        10.  §6.50.        11.  §52.50.        12.  §43.20. 

13.  §173.25.         14  §29.43.         15.  §15.40. 

Page  153. —  16.  §3.      17.  §  10.      18.  §19.50.      19.  $12.48.       20.  $6.80. 

21.  §7. (19. 

Page  154.— 2.  §63;  §363.  3.   §40.83;   §290.83.  4.   §34;  §194. 

5.  $4.17;  854.17.  6.  §152;    §952.  7.  §3.81;    §54.61.  8.    §.64; 

§16.64.  9.  §3;  §78.  10.  §35;  §455.  11.  $2.63;  §43.13.  12.  §8.76; 
§309.16.  13.  §4.08;  §104.08.  14.  $27.50 ;  §527.50.  15.  85;  §1005. 
16.  §3.23;   §63.83.  17.   $69.44;    $319.44.  18.    $15.64;    $91.44. 

19.  $251.25;  §1751.25.         20.   §24.85;  §150.35.        21.  §296.78;  $1436.78. 

22.  §130.68;  §1043.28.  23.  §701.17;  §3910.17.  24.  §48.22;  $682.72. 
25.    §297. 

Page  155.  — 1.  §33.         2.  §800.         3.  $3.         4.  30  girls.  5.   .0125; 

.125;  1.375;  .0625.    6.  §12.50.    7.  §64.    8.  §22.50.     9.  §  .83.     10.  §76.50. 

11.  8.24.     12.   §1.50. 

Page  156.  — 13.  §1.32.         14.  $45.         15.  $2.        16.  $420.        17.  $20. 

18.  20,UU0.         19.  §325.        20.  §3.        21.  §9. 

Page  158.  — 7.  §8.75.         4.  §274.32. 

Page  159. —1.  110,092.  2.  37.  3.  50.601.  4.  25.061;  125.5;  300.0002. 
5.  4742.         6.  .0119.         8.   8jL  10.  55.12.  11.  $.30.  12.   2771  It. 

13.  39  mi.  319  rd.  5  yd.  1  ft.  1  in. 

Page  160.  — 14.  §132.        15.  $2160.       16.  §103.74.        17.  2f.       18.   .1. 

19.  T",V  20.  §42.  21.  38104  mi.  22.  2|  T.  23.  §375.75.  24  §1080. 
25.  §"100.         26.  §272.50.         27.  56  A. 

Page  161.  —28.  §3892.50.  29.  §16.80.  30.  1  da.  2  hr.  53  min.  20  sec. 
31.  §750.  32.  §20.17.  33.  -^-,  -%7-,  ^,  §£.  34.  §288.  35.  2||ff  mi. 
36.  048,045  cu.  in. ;  375?}  cu.  ft,        37.  26$%  gain. 


ANSWERS  J.".1 

Page  162.  — 38.  8;  $1.60;  $20.83$.  39.  $5625.  40.  $  101.25. 

41.  $4.50.        42.2i)rd.        43.  $  707 J.        44.  $55.08.        45.  $2. 

Page  163.-  47.  156f  cu.  yd.  48.  4  rd.  1  ft.  <i  in.  49.  28  rd.  52.  §420. 
53.   10%.         54.  62.5  da.         55.  24  rd.         56.  48  people. 

Page  164.  —  57.  999.00199+.  58.  $16.88.  59.  177  rd.  4  yd.  10  in. 

60.  $8.  61.  2  1b.  8  oz.  62.  $  1900.  63.  1152  gal.  64.  8  30.  65.1}$. 
66.  John,  55  A.;  James,  110  A.  67.  ^  da.  68.  .0072.  69.  $46.20. 
70.  $.18. 

Page  165. —  71.  §193.33.  72.  50£$  A.  73.  1108.8  ft.  74.  81926. 
75.814.40.  76.  T%.  77.81800.  78.  $111.30.  79- 320  rd.  80.2.5. 
81.  $247.50.        82.  840.50.         83.  $20.97.         84.  Latter  by  §75. 

Page  169.  — 1.  8564.35. 

Page  170. —  2.  8257.53.        3.  $365.80.        4.  8213.17.        5.  $12,677.94. 

6.  86.20. 

Note.  —  In  business,  a  half  cent  or  more  is  usually  counted  as  an  addi- 
tional cent. 

Page  172. —  1.  8159.88.      2.8107.21.       3.  $17.87. 

Page  174.  — 1.  By  Bal.  87.87.      2.  By  Bal.  $97.68. 

Page  178— 3.  920  qt.     4.  218  pt.     5.  247  hr.     6.  2640  rd. 

7.  22, 160  min.   8.  33,585  lb.   9.  8765Tf£§  hr.   10.  924  in.   11.  423$  ft. 

12.  31,451.35  ft.  13.  184  oz.  15.  28  oz.  16.  112  pt.  17.  174,960  in. 
18.  280  rd.   19.  16  cwt.  80  lb.   20.  202  da.  18  hr.  40  min.    21.  128$  ft. 

22.  5  da.  6  hr.   23.  255  min.   24.  9768  ft. 

Page  179.  —  2.  56  gal.  1  qt.  3.  20  bbl.  7  gal.  2  qt.  4.  365  bu.  3  pk. 
5.  10  da.  10  hr.  6.  16  rd.  1  ft.  4  in.  7.  94  min.  35  sec.  8.  1  mi.  58  rd. 
4  yd.  1  ft.        9.  2  leagues.        10.  4  T.  2020  lb.         11.  45  rd.  3  yd.  2  ft.  7  in. 

13.  .02||  mi.       14.   .30025  T.       16.  &  ft. ;  ^  yd.       17.  f  lb. 

Page  180.  — 18.  f.       19.  .87+.      20.  820.36.       21.  $6.       22.   Ill  boxes. 

23.  150  qt.  24.  81.08.  25.  113,796  ft.  26.  8263.01.  27.  191  bottles. 
28.  9500  packages.     29.  81.65. 

Page  181.  —  30.   12,300  ft.  31.   429.14  lb.  32.    13  mi.  252  rd.  2  ft. 

33.  84. 

Page  183.  — 1.  $182.49.  2.  8130.27.  3.  8111.75.         4.  8170.33. 

5.  813(1.85.  6.  $73.34.  7.  8151.85.  8.  829.20.  10.  850.  11.  8131.62. 
12.  $481.64.  13.  $23.94.  14.  $425.89.  15.  8148.42.  16.  $20.22. 
17.8143.79.     19.   £  160  7s.  7.72d.     20.  500  marks.     21.  144  lire. 

Page  184.  —  3.    133  bu.  2  pk.  7  qt.  4.   97   hr.  52  min.    39  sec. 

5.  5  hr.  46  min.        6.  11  yr.  9  mo.  3  \vk.  5  da. 

Page  185.  —  8.    57  yr.   2  mo.    8  da.  9.    84  vr.    9  mo.    10  da. 

10.  42  vr.  11  nm.  12  da'.  11.  £2006  18s.  9d.  12.   £  1 14  10s.  Id.  ; 

£62  4.s\  lOd.  ;  £  192  9s.  id.       13.  32  hr.  40  min.       14.  5  T.  4  cwt.  15  lb. 

Page  186.  —3.  52  bu.  8  baskets.  4.  8  yd.  251  in.  5.  10,800  ft. 

6.  42  gal.  2  qt.  1  pt. 


452  ANSWERS 

Page  187.  —  "I.    Widow,    $9733.65;    children.    sr,840.19.  8.  $8.40. 

9.  5940  turns.     10.  $13.89.     11.  96  mi.  284  id.  4  yd.    12.  165  T.     13.  $9.30. 

14.  240  ft.  11  in.  ;  8  lb.  10  oz.  ;  27  bu.  2  pk.  5  qt.     15.  $115.07.     16.  $74.31. 

Page  188.  — 1.  $73.88.      2.  $305.50.       3.  f*.      4.   10  bbl.       5.  $166.88. 
6.   10,000.  7.  2|  doz.  8.  04.435.  9.  5~4.41^  mi.  10.  401.44  mi. 

11.  $.0311+. 

Page  189.  — 12.  55.07+  mi.  per  hour.  13.   191.75  1b.         14.  522.708^. 

15.  1071f  bu.  16.   If.         17.  $675.         18.  $47.50.  19.   .9775|7  min. 
20.  84.5375  mi.       21.  28.75  rd.       22.  1876  1b.       23.   7. 


Page  190.  —  24.  $3.85.  25.  100  bbl.  26.  $1000.  27.  3.74624625. 
28.  4131.  29.   .138.  30.  $8.50.  31.   136  books.  32.  $60,000. 

33.  $2018.75. 

Page  191.  —  34.  $350.  35.  $24,000.  36.  $9.10.  37.  $6000. 

38.  2111.101.  39.   849.404.  40.  6270.835.  41.  101,260.269. 

42.   1034.25478. 

Page  193.  —  1.  480  sq.  in.       2.  075  sq.  rd.       3.   .78125  A.       4.  60  sq.  rd. 

Page  194.  — 5.   174,240  sq.  ft.  6.   108  sq.  in.  7.   176,418  sq.  in. 

8.  256,000  sq.  rd.       9.   11  A.  40  sq.  rd.        10.   11  sq.  ft,       11.  294,030  sq.  ft. 
12.  94.31625  A.;  $29,473.83. 

Page  200.— 2.  246  sq.  ft.  3.   144.9  sq.  ft.  4.  2916  sq.  ft. 

5.  218.5  sq.  ft.  6.   517  sq.  ft.  72  sq.  in.  7.   045  sq.  ft.  8.   27  sq.  ft. 

9.  54  sq.  yd.      10.   180  sq.  yd.     11.  2400  sq.  yd.     12.  First  16  times  as  large 
as  second  ;  first  \  as  large  as  second.     13.  $30.94. 

Page  201.  — 14.  bj%  A.         15.  30  rd.         16.  3  lots. 
2.  $40.         3.  $7.89.         4.   89  bundles. 

Page  202. —  5.  $54.15.         6.  $305.21.         7.  $231.22. 

1.  $134.40.       2.   12,960  tiles. 

Page  203.  —  3.  40  sq.  in.  4.  360  slates.  5.  240  slates  ;  450  1b. 

6.  5760  slates;  $88.  7.   157  bundles.  8.  $172.38.  9.  $105. 

10.  30  squares. 

Page  204.  —  2.  15  rolls.         3.  $18. 

Page  205.  — 5.  55T^  yd.  ;  73^  yd.  6.  5,  5,  6,  6,  6.  7.  7,  6,  7,  8,  8. 
8.   $14.67.         9.  $45.84. 

Page  207.  —  2.    9  sq.  ft.         3.    140  sq.  ft.       4.    60  sq.  ft.       5.    150  sq.  ft. 

6.    450  sq.  ft. 

Page  208.— 1.   52*  A.        2.  28.4062  A.        3.  75.        4.  25  rd.        5.  7  rd. 

6.    80  rd. 

2.  7  sq.  ft.  42  sq.  in. 

Page  209.  — 3.    10  rd.         4.    30  rd. 

2.    440  sq.  ft.         3.    308  sq.  ft. 

Page  210. —  1.  47.124  ft.  2.  »78.54  ft.  3.  188.496  ft.  4.  33.5104  ft. 
5.  39.27  ft.  6.  78.54  yd.  7.  126.7112  ft.  8.  7.854  ft.  9.  82.7282  ft. 
10.    4  ft,         11.    40  yd. 


ANSWERS  453 

Page  211. —1.    78.54  sq.rd.  2.    314.16  sq.  rd.         3.    254.4696  sq.  rd. 

4.   1017.8784  sq.  ft.      5.  314.16  sq.  in.      6.  1256.64  sq.  in.      7.  5026.56  sq.  rd. 

8.  490.875  sq.  rd.        9.   6026.56  sq.  ft.         10.   .78  sq.  ft.        11.    3.14  sq.  rd. 

12.  706.86  sq.  in.  13.  962.11  sq.  yd.  14.  314. Hi  sq.  ft.  15.  78.54  sq.  yd. 
16.  49,087.5  sq.  ft.  17.  11,309.70  sq.  yd.  18.  1134.11  sq.  yd.  19.  21.46 
sq.  ft.        20.    $50.27. 

Page  213.  — 1.  432  sq.  ft.     2.  68  sq.  ft.  8  sq.  in.     3.  118  sq.  ft. 

4.  412  sq.  ft.   5.  170  sq.  ft,   6.  334  sq.  ft.   7.  706  sq.  ft.   8.  96  sq.  in. 

9.  6  sq.  ft.  10.  24  sq.  ft.  11.  6  sq.  ft.  73$  sq.  in.  12.  8  sq.  ft.  24 
sq.  in.    13.  88 J  sq.  yd.    14.  8  sq.  ft.  109|  sq.  in. 

Page  214.  —2.  250  cu.  ft.  3.  684  cu.  ft.  4.  800  en.  ft.  5.  9  cu.  ft. 
6.  4  cu.  ft.  1248  cu.  in.   7.  5  cu.  yd. 

Page  215.—  8.  213$  loads.  9.  1728  cakes.  10.  448  en.  ft.  11.  5  C. 
12.  22£C.  13.  64  boxes.  14.  22}  C.  ;  S41.63.  15.  23 $  C.  ;  $ 42.78. 
16.  28f  C.  ;  8 52.03.    17.  18|  C. ;  $34.69.    18.  106$  loads. 

Page  216.  — 19.  56 \  C.  20.  J7.  21.  1417$  cu.  in.  22.  111.475  cu.  in. 
23.  126.6  cu.  in.  24.  1621|  cu.  in.  25.  10,936f  cu.  in.  26.  1595|  cu.  in. 
27.  189  cu.  in.    28.  First;  1440  cu.  in.    29.  124||  cu.  in.;  451T9g  cu.  in. 

Page  218.— 2.  15  bd.  ft.   3.  24  bd.  ft.  4.  32  bd.  ft.  5.  180  bd.  ft. 

6.  96  bd.  ft.   7.  36  bd.  ft.   8.  150  bd.  ft.  9.  144  bd.  ft.  10.  432  bd.  ft. 

11.  360bd.  ft.    12.  2000  bd.  ft.     13.  720  bd.  ft.  14.  1200  bd.  ft. 

15.  240  bd.  ft.    16.  $21.60. 

Page  219. —1.  8419.06.  2.  828.  3.  847.25.  4.  $26.25.  5.  839.38. 
6.    8  10.50.  7.    960  bd.  ft.  8.    12,800  bd.  ft.  9.    3500  bd.  ft. 

10.  4800  bd.  ft.  11.  1600  bd.  ft.  12.  1500  bd.  ft.  13.  8000  bd.  ft. 
14.  21.000  bd.  ft.  15.  8750  bd.  ft.  16.  1200  bd.  ft,  17.  16,666f  bd.  ft. 
18.  18,200  bd.  ft.  19.  24,000  bd.  ft.  20.  7000  bd.  ft.  21.  3600  bd.  ft. 
22.    10.000  bd.  ft. 

Page  220.  —  23.    8837.         24.    81488.         25.    8118.56. 
1.    448  cords.         2.    805f|  cu.  yd. 

Page  221.  — 3.    lOOff  loads;  503if  loads;  201U  loads.  4.    86429.63. 

5.  488|cu.  yd.  6.    37,842  bricks.  7.   41,328  bricks.  8.    8364.80. 

Page  222.— 1.    753.984  sq.  in.         2.    1413.72  sq.  in.         3.    62.832  sq.  ft. 

4.  20.944  sq.  ft.  5.  8.3776  sq.  ft.  6.  282.744  sq.  ft.  7.  678.5856  sq.  ft. 
8.    155.5092  sq.  ft. 

Page  223.  — 10.    3180.87  cu.  ft.         11.    14,726.25  cu.  ft.  12.   4021.248 

cu.  ft.  13.   4712.4  cu.  ft.  14.    100.5312  cu.  ft.  15.    6031.872  cu.  ft. 

16.  12.5664  cu.  ft.         17.    235.62  cu.  ft. 

1.    803.56+  bu.  2.    520.71+  bu.  3.   448.83  gal.  4.    119.36+  bbl. 

5.  4.94+  bbl. 


Page  224. 
3.    29,687|lb, 

—  1.   7500  lb. 
4.    53331 

;  120  cu.  1 
bbl.         5. 

Et. 

072  1 

2. 

JU. 

l|f§  T.  hard 

;  i 

i9  T. 

soft. 

Page  225. 
10.   81|fT.; 

1.  50.         2 

sq.  in. ;  5832  i 

—  6.  5 

38?  T. 
.  15  ft. 
3U.  in. 

3. 
6. 

7.  471.24 

3280  tiles. 
918  boxes. 

^gal. 

4. 
7. 

8.   84.823.2  1b. 

WO  sq.  in.;  80  sq. 
216  cakes. 

9. 

in. 

1958.4  bu. 
5.  1944 

454  ANSWERS 

Page  226.  — 8.    264  sq.  in.         9.  $57,600.         10.  $800.  11.    $7168. 

12.  $398.47.        13.   63,910  bricks.         14.   $553.96. 

Page  227.  — 15.    1.32+ ft.        16.   294f i  T.        17.   72  yd.        18.   $113.47. 
19.   $24.70.       .20.    Grading  $798;  $52,800.         21.   60°.        22.    78°. 

Page  228.  —  23.  75°;  30°.  24.  76£°  ;  90°.   .  25.  80|°.        26.   A,  20.75 

acres  ;   B,  26.93+  acres  ;    R.  R.  2.32-  acres.  27.    100  revolutions. 

28.    26.6455  knots  per  hour.                 29.    $35.47.  30.    21  double  rolls. 
31.  345  sq.  ft.         32.   $100.45. 

Page  229.  —  33.    $424.96.  34.    15  ft.  35.    $96.36.  36.    $80. 

37    S666.67.        38.   $ 468.         39.  $826.20.        40.  2714.34  cu.  ft.  41.960 

blocks  ;  55.2  T.         42.    16.755  bbl.        43.    3  T.        44.   $72.50. 

Page  230.  — 45.    $663.51.  46.   $67.50.  47.   $322.22. 

48.   $167.68.         49.    2025  1b.         50.   $166.59.         51.    4  ft.  52.    $712.80. 

53.  1200  ft. 

Page  232.  — 2.    $8.        3.    30  sheep.  4.   60  yr.         5.    300.         6.    24. 

7.    100. 

Page  233.  — 11.    $11.  12.   $37.50.  13.   16  yr.  14.    30  books. 

15.80?.         16.  $100.         17.  $9000.         18.  $7.50.        19.  60  bu.        20.  $96. 

Page  234.  —  21.    $80,000.  22.   $480.  23.    $2400.  24.   $1000. 

25.  $24.         26.  $1.50.        27.   750  girls  ;  450  boys.        28.  12  yr.        29.  $24. 
30.    $300.         31.   30^.         32.   $5000.        33.    30  girls.        34.    $8000. 

Page  235—  35.  $75.        36.  $3200.        37.  18  mi.  first  day.         38.  $20. 
39.    18;  54.  40.    $150.  41.    $3000.  42.    $45,000.  43.    $540. 

44.    $5000;  $3000.        45.    £,  J. 

Page  236.  —  46.   T%.      47.   2|  da.       48.    12  da.       49.   6  da.        50.  4  da. 

51.   ft 48.  52.    Harness,    $20;   sleigh,    $40;    horse,    $160.  53.   $2. 

54.  $2700.         55.   $  da.         56.    Second,  $4200;  third,  $3000. 

Page  240.  — 2.    13.12.  3.    11.34.  4.   28.93.         5.   57.         6.   39.72. 

7.    20.45.         8.    236.16.        9.    5.4.       10.    25.         11.    ±.         12.    15.        13.  f. 

14.    147.       15.   112.        16.    180  girls  ;  220  boys.        17.   $7.50.       18.   25.2  T. 
19.   $2422.50.      20.   $16.50.       21.   The  same.        22.    $73.95*.        23.    $1750. 

24.  $292,702.50. 

Page  241.  —  25.  $2.60;  $1.73.      26.   $220,    John;  $198,  James;  $132, 
Henry.     27.   240  A.,  wheat ;  108  A.,  corn  ;  168  A.,  oats  and  grass  ;  84  A.,  rem. 

Page  242.— 2.    40%.          3.   374%.        4.    60%.  5.    75%.  6.    10%. 

7.  62i%.           8.   15%.  9.   60%."       10.    6±%.  11.    16|%.  12.    4£%- 

13.  14|%.       14.    200%.  15.    250%.         16.   360%.  17.   6%.  18.    90%. 
19.    15%.         20.   21%.  21.   4%.         22.    42%.  23.   56J%.  24.    280%. 

25.  7%.         26.    7i%-         27.   6%. 

Page  244.  —  3.   $30.         4.    $30.        5.    $728.         6.   $72.        7.   $127.50. 

8.  $1200.      9.   $11.25.       10.    $8.      11.   $56.80.     12.    $32.32.      13.    $4128. 

14.  $56.     15.  1)20  men.     16.  $1800.    17.   $4700.     18.    $50.     19.   600  pupils. 


ANSWERS  455 

Page  245.  —  2.  300.  3.  200.  4.  400.  5.  200.  6.  40.  7.  30.  8.  900. 
9.  300.  10.  $3.  11.  $2.  12.  $3500.  13.  $1000.  14.  *4700. 
15.   10  sq.  mi. 

Page  246.  — 2.  100.  3.  300.  4.  72.  5.  45.  6.  400.  7.  400.  8.  500. 
9.  5.  10.  $40.  11.  -sC.O.  12.  $384.  13.  $2000;  $800 ;  $10,000. 
14.    549  pupils.     15.    $20.     16.    J,j.     17.    1000.     18.    $100  loss.     19.    16,000. 

Page  247.  — 1.    100.         2.   20.         3.    1.      4.  $10;  12'%.         5.  $854.40. 

6.  50%;  10.     7.    300%;  331%    g.    50%.     9.    10fi%.     10."   340.     11.   $4000. 

12.  $500.     13.    if. 

Page  248—14.   85%.  15.    $14,175.  16.    120.  17.   $5. 

18.  37',  %;  2J%;  87.', ";.  19.  $ 200,  horse  ;$  100,  buggy.  20.  $12,000. 
21.  2  t.  22.  5%.  23.  $0000;  $7200.  24.'  $  144  ;  $150;  $180. 
25.    121%.         26.   $1732.50.         27.   60^. 

Page  249.  —  28.    $1620.     29.    $9250.     30.   $  2760,  increase.     31.    74f£%. 

Page  250.  —  2.    $15.       3.    $32.       4.    $17.25.       5.    $43.13.      6.    $74.76. 

7.  $37.10.      8.    $24.28.       9.    $  110.10.       10.   $260.      11.   $2.40.      12.   $540. 

Page  251.  — 2.   5%  gain.        3.    20%  gain.       4.   4%  loss.        5.    35%  loss. 

6.  30%  gain.        7.   33£%.         8.   20%.         9.    22?%.    '     10.   J  %  gain. 

Page  252.— 2.    $500.       3.    $300.  4.   $500.  5.    *2450.  6.   $8400. 

7.  $2500.  8.  $35.  9.  $225.  11.  .s200.  12.  S600.  13.  $880. 
14.  $960.  15.  $1020.  16.  $600.  17.  $11,600.  18.  $1250.  19.  $1.25. 
20.    $1.25. 

Page  253.  —  22.   $360.         23.    60'.'.         24.    2h%. 

1.  $4143.75.  2.  56}%.  3.  20%  gain.  4.  $88.  5.  $3000.  6.  $10,000. 
7.   $575.     8.    $800. 

Page  254.  — 9.  25%,.  10.  $30.  11.  $7500.  12.  4%  gain.  13.  12*%. 
14.    $2.70.         15.    $153.         16.   $8000.         17.   $150. 

Page  256.  — 2.    $68.75.  3.    $78.18.  4.    $365.75.         5.    $5484.38. 

6.    1%.       -7.   3%.         8.    2%.         9     2£%. 

Page  257.  — 10.   $09,040.80.         11.    $152.50.  12.   S624.        13.    $616. 

14.   $1250.          15.   $2268.          16.    $3280.          17.  $966.67.          18.    $3795. 

19.  $19,750.         20.    $1220.        21.    $520  gained.  22.    2%. 
1.    $16,200.         2.    S  7787.50. 

Page  258.  — 3.   $1010;  $1753.  4.    $6085.25.  5.    $306. 

6.  $  1595.80  agent's  commission  ;  10^  %  gain.        7.    $210.75. 

1.   Com.,  $54;  net  pro..  $609.76.  2.    Rate,  4°/  ;  net  pro.,  $524. 

3.   Gross  sales,  $  1000  ;  c .,$200.  4.    Rate,  10% ;  net  pro.,  $504. 

5.   Gross  sales,  $600;  rate,  8%.  6.   Cora.,  $40;  net  pro.,  $960. 

7.  Grosssales,  $6700;  expenses,  none.  8.    Rate,  2%;  net  pro.,  $2404. 

Page  259.  —  9.   $1851.35.     10.  360  A.     11.  $131.60;  $6580.    12.    $1680. 

13.  $23,294.12. 

Page  260  —  2.    |%;$24.  3.   $58.50.  4.    2J  %;$  2.50  per  $  100. 

5.    |%.         6.    23^.         7.    $1900.        8.    1|%. 


456  ANSWERS 

Page  261.  — 9.    $53.25.      10.    «  12,000.      11.    1%.      12.    \\%     13.    $42. 

14.    Farmer's  loss,  $210;  company's  loss,  $3290.  15.    Company's  loss, 

$17,415  ;  owner's  loss,  $0585.  16.  $4800.  17.  First,  $  18,000  ;  'second, 
$21,600  ;  third,  $32,400  ;  fourth,  $36,000. 

Page  263. —  1.    $119.80.  2.   33^|f%.  3.    48525%.         4.   $821.60. 

5.  $268.45.         6.    45  yr.         7.   $800.40.         8.    $450.55. 

Page  264. —1.   $3;  trade.   2.  Time  and  cash.    3.   10%;  trade.    4.  $125. 

Page  265.  —  5.  30%;  trade.  6.  Trade.  7.  Time,  $3.75 ;  cash,  $7.50. 
9.    $15.         10.    $30.         12.   $10.         13.    $1350.         14.    10%  cash. 

Page  266.  —  4.  $56.70.  5.  $72.  6.  $144.  7.  $20.60.  8.  $8. 
9.   $238.03.         10.   $83.79.         11.   $223.13.         12.    $273.60.        13.   $3249. 

Page  267.  — 14.   $175.  15.    $231.60.  16.    24£ if  %.  17.    $1. 

18.  First,  $2.50.  19.  No  difference.  20.  Third  is  $208  better  than  first 
and  $  135  better  than  second.       21.    $70.13.      22.    $1525.95.         23.   66.8%. 

Page  268.  — 2.    $547.20. 

Page  269.  —  3.   $564.48.         4.    $39.34. 

Page  271.  —2.  Taxes,  $38  ;  poll  tax,  $3.  3.  Taxes,  $236  ;  poll  tax, 
$4.  4.  3£  mills,  rate.  5.  Est.  val.,  $937.50  ;  assessed  val.,  $  750.  6.  Est. 
val.,  $222,900;  assessed  val.,  $148,600.  7.  18  mills  ;  $225.  8.  $19.75. 
9.    $8125.         10.    8  22,460;  $561.50. 

Page  272.  — 11.   $74.70.       12.   $65.60.       13.    $4680.        14.    $21,173.64. 

Page  273. —  1.    $198.         2.    $2500.         3.   8  6000.        4.   $144. 

Page  274.  —  5.   $800.  6.    $728.  7.    8  2687.50.  8.    3860  1b. 

9.   $2665.60.         10.    $4.3045  per  dozen.        11.   8 11,629.75.       12.   $3289.49. 

13.  $2673.     14.    1600  yd. 

Page  276  —  2.    $37.50.  3.   $198.24.  4.    $45.50.  5.   $40. 

6.  $19.50.      7.    888.      8.    8129.      9.   $11.        10.   $41.80.      11.   $56.55. 

Page  277.  — 2.    $1675.80.         3.    8  1226.55.         4.    $448.  5.    $573.80. 

6.  83585.  7.  81439.3(1.  8.  $215.12.  9.  82287.81.  10.  $2952.50. 
11.  $225.50.  12.  81342.33.  13.  $122.66.  14.  $4056.50.  15.  $210.43. 
16.  8342.91.  17.  $233.14.  18.  $1087.75.  19.  $167.67.  20.  $656.43. 
21.    $58.68.     22.    $314.61.     23.    $110.89.     24.    $53.79.     25.    $56.28. 

Page  278.  —  2.    $2.75.      3.   $1.43.       4.    $2.58.       5.    $2.97.     6.     $7.13. 

7.  $4.20.     9.    *2.50.      10.    $3.80.     11.    $13.02.      12.   $2.50.      13.   $10.06. 

14.  $5.31.     15.    $2.50.     16.   $2.10. 

Page  279.  —  17.   $18.           18.    $15.75.           19.   $42.75.  20.   $60.50. 

21.  $57.60.         22.    s  13.05.          23.    $57.96.         24.    $12.64.  25.   ft  44.96. 

26.  $13.40.     27.  $9.99.     28.  ft 30.     29.  $34.88.     30.    $31.10.  31.    $59.50. 

32.  $31.36.          33.   $25.34.          34.    $33.80.          35.    $8.85.  36.    $2.25. 

37.  $13.      38.    $2.67.      39    $3.01.      41.   $16.25.     42.    ft  10.83.  43.   $9.60. 

44.  8  7.13.            45.    $30.75.            46     $2.90.            47.    811.  48.    $.51. 

49.  $3.07.     50.  ft  7.05.     51.   $13.24.     52.86.71.     53.    $11.23.  54.   $80.03. 

55.  $171.81.      56.    $9.90. 


ANSWERS  4.r>7 

Page  280.  —  57.  $1500.75.  58.  $121.60.  59.  $207.80.  61.  827.54. 
62.  $74.30.  63.  $74.80.  64.  $160.05.  65.  $306.10.  66.  $144.15. 
67.    $202.0(1.     68.    $20.50. 

Page  281 .  —  2.  $115.48.  3.  $91.  4.  $65.33.  5.  $101.28.  6.  $4.58. 
7.    $9.     8.    $19.85.     9.    $114.49.     10.    $73.02.     11.    $77.25.     12.    $169.30. 

13.  $337.40.  14.  $219.75.  15.  $247.50.  16.  $2.40.  17.  $4.77. 
18.  $6.18.  19.  $10.50.  20.  $47.60.  21.  $60.50.  22.  $38.25. 
23.   $145.13.     24.    $10.66.     25.   $19.99. 

Page  282. —  26.  $31.93.  27.  $36.56.  28.  $1312.19.  29.  $966.60. 
30.  s  151.59.  31.  $896.13.  32.  $415.28.  33.  $38.48.  34.  $207.81. 
35.  $2246.44.  36.  $7.16.  37.  $18.27.  38.  $12.33.  39.  $22.25. 
40.  $77.19.     41.  $9.61.     42.   $1423.15.     43.  $705.53.     44.  $4044.     45.  $134. 

Page  283.  — 2.   $1000.     3.    $680.     4.    $1200.     5.    $1375. 
2.    0°/0. 

Page  284. -3.   5%.     4.   5%.     5.    6%. 

2.    3  yr.  4  mo.     3.   20  yr. ;  16f  yr.  ;  12}  yr.      4.  40  yr.     5.    Oct.  13,  1902. 

1.  $31.44.     2.    2  yr.  6  mo.     3.    3  yr.  6  mo. 

Page  285.  —  4.    41%.  5.    $434.         6.    $180.  7.   $275.         8.6%. 

9     In  3  vr.  4  urn.     10.  $354.31.     11.   $  88.20.     12.  Jan.  19,  1906.     13.  $600. 

14.  July  1,  1906.     15.    $86,700.     16.    $3025. 

Page  286.  —  2.    $116.19.     3.    $8292.48. 

Page  287.-4.  $4954.20;  $495.42. 

2.  $10.26.  3.  $35.29.  4.  $60.49.  5.  $41.34.  6.  $11.10.  7.  $20.68. 
'8.  $299.18.     9.    $116.99.     10.    $88.70. 

Page  288.  —  11.   $396.40.      12.    $-655,912.33. 

Page  289. —2.   $103.81.     3.  $10.45.     4.   $27.41. 

Page  290.  —  2.    $1.52.     3.    $157.99.     4.   $80.52.     5.    $1056.07. 

Page  291.  —  6.    $206.04.     7.   $160.60.     8.    $909.93.     9.    $1233.35. 

Page  292.  — 1.   $1526.74.      2.    $14,233.12.     3.   $5642.40.     4.   $1324.90. 

Page  298.  — 1.    $103.  2.   $255.44.  3.    $630.42.  4.    $367.44. 

5.    $129.13.      6.    $1219.50.       7.   $316.60. 

Page  301.  —  2.   $669.20.       3.    $295.65.      4.    $110.17. 

Page  302.  —  5.    $355.64.      6.   $9.57. 
1.    $  439.70.       2.    $2380.37. 

Page  306. —1.  $663.15.       2.  $399.70,  balance. 

Page  309.  —  2    *203.       3.    $200.       4.    30;6<*. 

1.    Aug.  1.  2.    Aug.  22.         3.    Nov.  13.  4.    Oct.  10.  5.    April  2. 

.May  17.         7.    June^lO.         8.    Sept.  5. 


tj 


458  ANSWERS 

Page  310.  —9.  April  30.  10.  July  10.  11.  Nov.  10.  12.  June  23. 
13.    Oct.  14.        14.  April  2.         15.    July  23.         16.    Dec.  7.  17.   Sept.  3. 

18.    Oct.  24. 

3.  Nov.  8;  $2.25;  $2.28.  4.  Aug.  12  ;  $  5.67  ;  $5.76.  5.  Oct.  2  ;$  11.50; 
$11.63.  6.    May  8;  $15.63;  $15.76.  7.   April  24  ;$  4.75;  $4.85. 

8.    July  17  ;  $4.53;  $4.59.  9.   Oct,  1  ;$  8.50  ;$  8.78.  10.   March  11; 

$6.46;  $6.53.       11.    May  16  ;$  15.75  ;$  15.97. 

Page  312. —1.    $2487.92  ;  $2487.50.  2.    $  1568.89  ;$  1568.63. 

3.  $  1545.70  ;$  1545.44.         4.    $  4521.82  ;  14521.06. 

Page  313.  —  5.  $  4455  ;  $  4454.25.  6.  $  3468.50  ;  $  3467.92.  7.  $  3537.87  ; 
$3537.27.  8.    $1000.  9.    $  1207.04  ;$  1206.83.  10.    $200;  $200. 

11.   $209.     12.    $  205.62  ;$  205.59.      14.    $224.33.      15.    $  259.21  ;$  259.10. 

Page  314.  — 16.  9%.  17.  12%.  18.  $  158.76  ;$  158.73.  19.  $1828.04; 
$1827.74.  20.  $1217.22;  $1217.01.  21.  $  2467.50  ;$  2467.08.  22.$6375.81; 
$6374.98.       23.   $1000.       24.   $2800. 

Page  319.  —  1.   $  550.80.  2.    $  1575,  face  ;  $  2.63,  exch.  3.  $  1.30. 

4.  15?.       5.   $  1078.92. 

Page  320.  —7.  Face,  $989.01  ;  exch.,  $.99.  8.  Exch.,  $  12.75;  com., 
$275;  face,  $12,747.75.        9.   $791.98.         10.    $311.85. 

Page  322.  —  1.   60  da.;  61  da.        2.    $1183  ;  $1182.77. 

Page  323.  —  4.    $  11,016.75  ;  $11,014.59.  5.    $591.80  ;  $591.70. 

6.  $3809.50.         7.   $2456.25;  $2455.83. 

Page  326.-2.  $6067.50.  3.  $8987.  4.  $12,142.  5.   $11,355. 

Page  327. —6.  $19,936.  7.  $8656.25.  8.  $20,680.63.  9.  $66,187.50. 
10.  $37,250.  12.  240  shares.  13.  8  shares.  14.  100  shares.  15.  40 
shares.       16.  44  shares  ;  surplus  $  14.50.       17.  61+  shares  ;  surplus  $54,625. 

Page  328.-3.  $825.        4.  $1892.63.         5.  $2153.13.         6.  $22,137.50. 

7.  $7453.13.        8.  $26,784.         9.  $13,785.         10.  $23,490. 

Page  329. —12.  120  shares.  13.  112  shares.  14.  40  shares.  15.  168 
shares.        16.  200  shares. 

1.  $60.  2.  $80.  5.7%.  6.5%.  7.  $2000.  8.  $16,000; 

$800. 

Page  330.-10.  4%.  11.6%.  12.  4J%.  18.6$%.  14.6}%. 
15.8%.      16.  Less.       18.  $1185.      19.  Former,  T\%  better.       20.  12J  %. 

Page  331.  — 21.  $800,000.  22.  $288.  24.  $24,025.  25.  $7288.75. 
26.  $36,556.88.     27.   $9446.63. 

Page  333. —  1.  $15,581.25.  2.50.  3.  $30,000.  4.  $2000. 

5.  $35,437.50.        6.   12%. 

Page  334.  -  7.  6\  %.  8.  6 %.  9.  $  1487.50.  10.  6£  %  ;  5| %  ; 

5%;  4J%;  4%.         11.  $4000.         12.  $1584.48.         13.  $400.        14.  500%. 

16.  5ry/0. 

Page  335. —1.  $00.48.  2    $635.04.  3.  $8870.  4.  30|%. 

5.  §520.52;  $520.42.         6.   $36.40.         7.   $4000.  p458 


ANSWERS  459 

Page  336.-8.  19$%.  9.23+%.  10.  $212.50.  11.  6|%.  12.  16^%. 
13.  $585.     14.  $1282.50;  commission,  $67.50.     15.  $480.     16.   $7100. 

Page  338. —  1.  5.      2.  .25.      3.  3.      4.  &.      5.  8.      6.  .4.      7.   fa.      8.  \. 

9.  100.     10.  3.     11.  0.     12.  320. 

Page  339.-3.  18f.  4.  15.  5.  10.  6.  5.  7.  5.  8.  10.  9.  I.  10.  .5. 
11.  2.5.     12.  90.     14.  30  da.     15.  $  18.     16.  50  da. 

Page  340.  — 17.  8.  18.  $1021.88.  19.  $4.17.  20.  4  oz. 

21.  41  j  mi.  22.  $40.  23.  $70.55.  24.  4  da.  25.  37 Z  sec.  26.  3875 
letters.     27.   180  ft.     28.  31,250  bricks. 

Page  341. —29.  36||  mi.  30.  30  men.  31.  24  men.  32.  $60.30. 
33.  38  cars.     34.  $236.25. 

Page  342. — 2.  $81,  man;  $  54,  first  boy  ;  $27,  second  boy.  3.  Expenses, 
$5200;  net  savings,  $10,400.  4.  $672,000;  $28,000;  $42,000;  $03,000. 
5.  Lake,  $1000;  railroad,  $  1800.     6.   $60,000;  $230,000. 

Page  343.-2.   A's,  $2520  ;  B's,  $5700  ;  C's,  $4320.  3.   M's,  $2520; 

N's,  $3024  ;   K's.  $2010.  4.    E's,  $1000  ;     F\s,  $857i  ;    G"s,  $2142f 

5.  $1329r6r;  $920T\.     6.  Smith's,  $3225;  Jones's,  $4300;   Brown's,  $2150. 

Page  344.-8.  $3348  to  N  ;  $40">8  to  M.  9.  R's,  $1053.75  ; 

S's,  $1496.25.         10.  A's,  if  ;  B's,  |§. 

Page  345. —1.  $600;  $400.  3.  $3200;  $4000.  4.  $15,000;  $12,000. 
5.   50%;  25%;  150%.     6.  Frank,  $  18  ;  Henry,  $15. 

Page  346. —7.   Walter's,  $1.20;    Philip's,  $1.50.       8.40%.       9.  $5000. 

10.  Brown's,  $1050;  Long's,  $1200.  11.   $375.  12.  $450. 

13.  Moore's,  $1200;  Silven's,  $1800;  Rogers's,  $1500.  14.  $45  per  month. 
15.  77  da.         16.  To  A,  $2700  ;  to  B,  $2400. 

Page  347.  — 17.  $48.  18.  6  da.  19.  9  lots.  20.  48  persons. 

21.  100  A.  22.  600  per  dozen.  23.  24  da.-  24.  $3200  ;  $3000. 

25.  $1250.         26.  $500;  $000. 

Page  348.-27.    F,  $1440;  E,  $900.     28.  $500;  6%.  29.  500,   5000. 

30.  15  da.  31.  $32.  32.  $320.  33.  $1000.  34.  20,000  bu.  35.  $5. 
36.  Claim,  $1000  ;  loss,  $400.         37.  &  greater. 

Page  352.  —2.   15°  ;  1  hr.  ;  60°  W.  has  earlier  time.  3.  45°  ;  3  hr.  ; 

120°  W.        4.  60°  ;  4  hr. ;  15°  W.        5.  30° ;  2  hr.  ;  30°  E.  6.  105°  ;  7  hr.; 

75°  W.  7.  150°;  10  hr.  ;  120°  W.  8.  120°;  8  hr.  ;  90°  W.  9.  105°;  7  hr.  ; 
30°  E.     10.   105°  ;  7  hr. ;  45°  \V.     11.  30° ;  2  hr.  ;    15°  E. 

Page  353.  —  12.  10  hr.  8  min.20  sec.  a.m.     13.   11  hr.  17  min.  45£  sec.  a.m. 

14.  8  hr.  58  min.  29£  sec.  a.m.  15.  5  hr.  17  min.  33  sec.  p.m.  16.  5  hr. 
58  min.  \§  sec.  p.m.  17.  6  hr.  36  min.  49f  sec.  a.m.  18.  0  hr.  1  min. 
46^  sec.  p.m.  19.  12  min.  11|  sec.  p.m.  20.  11  hr.  48  min.  4  sec.  a.m. 
21.  5  hr.  47  min.  7^  sec.  22.  N.Y.,  3  hr.  36  min.  71  sec.  p.m.  ;  Cape 
Town.  9  hr.  40  min.  3  sec.  p.m.     23.   2  hr.  39  min.  35/.  sec. 


460  .  ANSWERS 

Page  354. — 26  Honolulu,  6  hr.  28  min.  37|  sec.  a.m.  ;  Berlin,  5  hr. 
53  min.  34j|  sec.  p.m.  ;  San  Francisco,  8  hr.  60  min.  17£  sec.  a.m.  ;  Lon- 
don, 4  hr.  59  min.  3G|  sec.  p.m. 

1.  17  da.        2.  21  da. 

Page  355.  —1.3  hr. 

Page  357.-5.   160  A.       6.  80  A.       7.  40  A.       8.  320  rd.       9.  480  rd. 

Page  359.-8.  225.  9.  256.  10.  324.  11.  484.  12.  625.  13.  42.25. 
14.  .5625.  15.  2J$.  16.  272£.  17.  225  sq.  in.  18.  625  sq.  ft. 

19.  256  sq.  yd.  20.  72£  sq.  ft.  21.  25  sq.  in.  22.  72.25  sq.  in. 
23.  100  sq.  yd.  24.  32^  sq.  yd.  25.  36  sq.  in.  26.  512  cu.  in.  27.  8  cu.  ft. 
28.  34§£  cu.  ft.     29.  42|  cu.  ft.     30.  56#6  cu.  ft.     31.  1876  Jy  cu.  ft. 

Page  361. —2.  15.  3.  24.  4.  21.  5.  14.  6.  40.  7.  28.  8.  36. 
9.  16.  10.  48.  11.  35.  12.  42.  13.  24.  14.  56.  15.  18.  16.  20. 
17.   72.       18.  25.       19.  32.       20.  64.       21.  27. 

Page  364.-5.  22.  6.  24.  7.  26.  8.  31.  9.  33.  10.  43.  11.  51. 
12.  63.      13.   |.      14.  if.      15.  |f.       16.  .5.       17.  .15.       18.  2.1.       19.  2.5. 

20.  .25.  21.  J7.74+.  22.  22.91+.  23.  34.  24.  66.  25.  14.5.  26.  13.35+. 
27.  122.  28.  163.  29.  369.  30.  4.56.  31.  9.84.  32.  13|.  33.  23.25. 
34.   56.5.     35.  75.12+.      36.  .92.      37.   .114.      38.  .02+.     39.  .66+.     40.  335. 

Page  366.-2.  32.45+ in.  3.  3  ft.  4.  32  ft.  5.  25  yd.  6.  44.72+ in. 
7.  8.94+ ft.  8.  1300  sq.  rd.  9.  22.36+ ft.  10.  42.42  mi.  11.  21.21+ rd. 
12.   1.41+ ft.         13.  45  ft. 

Page  368.  — 1.  370.8  sq.  ft.        2.  28.28  rd.        3.  97.425  sq.  in. 

Page  370.  — 1.  250  sq.  ft.  2.   17^  sq.  ft.  3.  108.3852  sq.  ft. 

4.  613.3974  sq.  in. 

Page  371.  — 1.   169.6464  sq.  ft.  2.    768  sq.  ft,  3.   161.9  sq.  ft. 

4.    700  sq.ft.  5.  854.17.  6.   *58.81. 

Page  372.  —1.  452.3904  sq.  in.  2.  28.2744  sq.  in.  3.  530.9304  sq.  in. 
4.  50.2656  sq.  in.         5.  •$17.45. 

Page  373.  —  1.   128  cu.  in.     2.  2  cu.  ft,      3.   185.4  T.     4.   190.8522  cu.  ft. 

Page  374. —1.  201.0624  cu.  in.  2.    9  times.  3.    1440  cu.  in. 

4.  3456  cu.  in.       5.  256  cu.  ft.       6.  600  cu.  ft.       7.  284+  bu. 

Page  375.  —  8.    4071.5136  cu.  ft.       9.  2ff  T.       10.   24  in.        11.  10  ft. 

1.  904.7808  cu.  in.      2.  268.0832  cu.  in.       3.   288.696+  cu.  in. 

Page  377.  — 1.   75  ft.       2.   80  rd.       3.    12  ft.       4.  2^.       5.    8  ft. 

Page  378.-6.  $8.67.       7.  21ft. 
1.    b 

Page  379.  -  2.  T\.  3.  ^f ,,  4.  fr  6.  20  ft,  ;  13$  ft,  ;  8  ft,  7.  16  ft. 
9.   200  cu.  in.       10.    179^  bu. 


ANSWERS  461 

Page  380. —4.   172.51b.       5.    C'.o.js     lb.        6.    1501b.       7     1046.20+ lb. 

8.  650.25  lb.  9.  64.375  lb.  10.  -",7..")  lb.  11.  556.25  lb.  12.  168.75  lb. 
13.849.3751b.      14.    1206.251b.      15.   151b.      16.   556.25  1b.      17.   700.25  11.. 

18.  181.251b.  19.487.51b.  20.455.6251b.  21.489.3751b.  22.  10K.75  lb. 
23.   114.375  lb. 

Page  381. —1.  27.08  bbl.  2.  1000  sq.  in.  3.   10.39+ in.  in  diam. 

4.  3.4724  ini.     5.  23  A.     6.  0257  i  bu.     7.  672.3024  cu.  in.      8.  4.18+ sq.ft. 

9.  18.1:5-  gal.       10.   1  to  2|. 

Page  385—  5.    1.363  in.  ;  13.00025  m.     6.   1  Km.  088  m.     7.   177.102  mi. 

Page  386.-8.  37.5  in.  9.   67.5906  mi.  10.  6  Mm.  ;  5  Dm.;  1  m. 

11.  (1400  Km. 

Page  388.-2.  s  72.00.  3.  87.50.  4.  24  sq.m.  5.  24  steres. 

Page  390.  — 1.  937.51.  2.   188,4961.;   188.496  M.  T.  3.  $159.23. 

4.  3,000,000  1.         5.   7.2  111.         6.  9000  bottles. 

Page  391. —  7.  838(50.  8.    154.56  pf. ;  $.3678.  9.   1000  1. 

10.  89TlT  Kg.  11.  1.3591+ cu.  m.  12.  3941.4  Kg.  13.  169.164  m. 
14.  863.75.  15.  811, 812.50,  cost  of  land;  81100,  cost  of  fence. 
16.  000,000  tiles.     17.   140.400  M.  T.         18.  4080  cu.  m.         19.  8  1.20. 

Page  392. —  1.  86.10.  2.  80.33.  3.  84.04.  4.  82.31.  5.  83.30. 
6.  811.74.      7.   811.93.      8.   812.06.      9.   8  13.48.      10.828.10.      11.   s4.21. 

12.  812.01.       13.  81.93.       14.  8  3.80. 

Page  393.  — 16.  1  to  7.0+.  17.  1  to  3.8+.  18.   1  to  5.27+. 

19.  1  to  5.05*.         20.   1  to  5.8+.         21.  1  to  8.7+.         22.   1  to  13.7+. 

Page  394.  —  23.  1  to  5.08+.  24.  1  to  7.69+.  25.  1  to  8.8+.  26.  Too 
wide:  lto7.1+.  27  Too  wide  ;  1  to  10.09+.  28.  Too  wide;  1  to  8.2+. 
29.  Too  wide  ;  1  to  10.3+.       30.  1  to  6.04+.       31.    1  to  4.06+. 

Page  396.  — 1.  234  lb.  ;  01.2  lb.  ;  52.25  lb.  ;  184  lb.  2.  .75  lb.  ;  1.14  lb.  ; 
10.875  1b.  3.  39. tons.  4.  285  tons.  5.812.25.  6.8  23.16.  7.824.33. 
8.  36.4  tons. 

Page  397.  — 1.   300  1b.  of  each.  2.82.60.  3.  $62.  4.8274. 

5.  §  1 140. 

Page  398—6.  8131.80.  7.  $1.  8.   $1.14.  9.  814.14. 

10.  Materials:  .000+  per  gal. ;  8  .115  per  tree.  Labor:  8  .01+ per  gal. ;  8.13 
per  tree. 

Page  399—11.  8.00.  12.  86.25;  81.28.  13.  830.19.  14.  300  gal.  ; 
7*  lb. 

Page  400.  — 15.    $9.80.      16.    $.072-  ;  84.28.      17.   $58.33.      18.   22$%. 

Page  401. —  1.  $1007.17.  2.  3.1416  sq.  rd.  3.  25.42+ in.;  42.42+ in. 
4.  $18.     5.  324  cu.  ft. ;  10.8  min.     6.  $200.72. 

Page  402.  — 7.  0  times.  8.   $300.  9.  8  2.88.  10.  f  22.62. 

11.  7.0086  cu.  ft,  ;  21.2058  cu.  ft.  ;  14.1372  cu.  ft.  12.  :!  mills. 
13    104.4  mi.      14.  00  lb.     15.   $2000. 


462  ANSWERS 

Page  403.  — 16.   Cow,    $50;  horse,    §140.  17.    150.7968   in. 

18.  4ii  rd.  ;  160  rd.       19.  BJ  %.        20.  33$%.  21.   17.32  in.        22.  22.36  in. 

23.  Width,  i»  ft.;  height,   6   it.                 24.   1  to   3f.  25.  8  834.40. 
26.  813,453. 

Page  404. —27.  8  1080.  28.  82000.  29.  8181.43;  8181.40. 

30.   $  175.  31.  20  A.  32.  A's,  320  A.  ;  B's,  480  A.  ;  C's,  600  A. 

33.  4.31+%.        34.   8630.40;  8630.29;  8639.86;  8639.75.        35.  81119.57; 
81118.87. 

Page  405.— 36.  852.17.  37.  85$  ft.  38.  848.72.  39.  8  570. 

40.   73.24+ ft.         41.  25.         42.  887.14.        43.  5  02+%. 

Page  406. —1.  60%.  2.  28?;  $2.80.  3.  830,000.  4.   100%. 

5.  6|hr.        6.  6i%.        7.  $1.65.        8.  31ft %• 

Page  407.  — 10.  M's,  8900;  N's,  8800.  11.  240  A.  12.  20%. 

13.  10  ft.     15.  300  crates.     16.  8120.     17.  40.15%.      18.  836.      19.  1081%. 
20.    6i%. 

Page  408.  — 21.  64  cu.  in.  22.  4%.  23.  A's,  8450  ;  B's,  8600  ;  C's, 
$1050.  24.  $1400;  8  1500.  25.  84500.  26.  8  25,000.  27.  a.  37$;  b.  f. 
28.31%.  29.  5456  yd.  ;  8342.4  yd.  30.8393.67.  31.8  2510.  32.32,768. 
33.   a.  4*  ;  b.  10^. 

Page  409.  —34.  *  3600.  35.  288  cakes.  36.11,011,011.000011. 

37.  3f.        38.   1121.112.        39.  8250,000.        40.  40  A.        41.   .4,    .375,    .28, 
.5625,  .75,  .15625.  42.  8  419.85.  43.  24,  15,  f,  2.  44.  84800. 

45.  84.32.         46.   12$  mills. 

Page  410.  —47.  60  da.,  8986.67  ;  61  da.,  8986.45.  48.  20^  sections  ; 

8  2880.     49.  $429.84.     50.  8  505.     51.  86.75.     52.  July  1,  1906.     53.   8  450. 
54.  8  705.     55.  A,  T23  ;  B,  £.&.     56.  8353.     57.  8168.48. 

Page  411. —58.  60  shares.  59.  20  vr.  ;  16f  yr.  ;  121  yr.  60.  8396. 
61.  8  313.04.  62.  8  .921  per  yard.  63.  8  336.  64.  14011b.  65.  819.20. 
66.  8  2949.60.       67.  21  mi. 

Page  412.— 68.  16.568  rd.  69.  75%.  70.  83$%.  71.  6283.2  sq.  ft. 
72.  $39.90.  73.  13 J*.  74.  2  yr.  4  mo.  75.  1000  cu.  ft.  76.  $39.25. 
77.  8887.50. 

Page  413.  — 78.  Second,  $15.  79.  8120;  20%.  80.  6%.  81.  81000. 
82.  s 38.40.  83.  First,  $13.50.  84.  $6.  85.  A,  1^5  ;  B,  f.  86.82125.60. 
87.  143%. 

Page  414.  — 88.  827,984.  89.  1020.021.  90.  413.875  1b.  91.  8500 loss. 
92.  8  4500  ;  81275.  93.  Latter  by  §  %.  94.48.55.  95.8  800.  96.  15  mills. 
97.  630  Kl.  ;  630,000  Kg. 

Page  415.  — 98.  10,000  A.  99.  Nitrogen,  1890;  oxygen.  7110. 

100.  $140.14         101.  200  men.       102    4V&.       103.  .0125.        104.  8  643.40. 
105.   $345.60.       106.  50  rd.       107.  8  6000. 


ANSWERS  463 

Page  416.  —  108.    836,720.  109.    Ninety-nine   hundred-thousandths. 

110.    Hi  ft.        111.    $4.         112.    $2842.50.         113.    $144.  114.    $601.50. 

115.    4 yr.  9  mo.  22  da.     116.    $540.     117.   9720  shingles. 

Page  417.  — 118.   34%.  119.    §640.  120.    $120.  121.    $6000. 

122.  162.5  1b.  123.  79.5.  124.  47!'|'/0.  125.  §300.  126.  §320.-.".. 
127.    $  3554.40  ;$  3655.     128.   500  ft. 

Page  418. —  129.  $  1979.74  ;$  1979.35.  130.  $513.44.  131.  $404.22. 
132.    $2937;  $2936.33.     133.    $1(370.14.     134.    §2(57.48. 

Page  419. —  135.  11  hr.  33  min.  57  sec.  a.m.  136.  $384.  137.  $1550, 
gain.  138.  $558.33.  139.  57.7269  Kl.  140.  39  Kg.  141.  $3213.42. 
142.    Dec.  7,  9  hr.  51  min.  0  sec.  a.m.     143.    1  mi.  22:!  rd.  (i  in. 

Page  420.  — 144.  120.  145.  8  2:171.85.  146.  70.  147.  $2298.75. 
148.    §1032.82.     149.    $83,144.91.     150.   §125,000.     151.    §2090. 

Page  422.  — 2.    $285.       3.    $450.       4.    $350.       5.    $441.51.        6.    $100. 

7.  $  11.25.     8.  The  former  is  §  5  Letter. 

Page   424.-4.    §120.25.  5.    $64.45+.        6.   $  1247. GO.       7.    $1228.96. 

8.  §148.95.  9.  $76.43+.  10.  $1948.  11.  12,921  fr.  87.5  c.  12.  $  2GG.48. 
13.  $2697.50.  14.  §457.90.  15.  6489  M.  80  pf.  16.  £309  lis.  lid.  ' . 
17.    §1478. G4;  1260  francs. 

Page  425.  —  2.    $90.     3.    §140.     4.    54  rd. 

Page  431. —  1.  14.  2.  16.  3.  24.  4.  27.  5.  32.  6.45.  7.  72. 
8.  98.  9.  123.  10.  1.  11.  I'i.  12.  r\.  13.  .9.  14.  2.5.  15.  3.4. 
16.    6.1,     17.    .15.     18.  'lh 

Page  432. —  1.  18  in.  2.  441  sq.  in.  3.  13  ft.  4.  47.55+ in.  5.  8  ft. 
6.  6  in.  7.  12  in.  8.  17  ft.  9.  5  to  7.  10.  18  ft.  high.  11.  The  base 
of  the  bin  is  172.8+  in.  square  ;  the  height  of  the  bin  is  86.4+  in. 


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